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

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

MT19937


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




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

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

MT19937


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

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

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

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

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


-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

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

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:04:43.36

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

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

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

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

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.03

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

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

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.36

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

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

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.71

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

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

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

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

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.05

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

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

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.63

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


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

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

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

Stat. AD after spacings (mNP2-S)      :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


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

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

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

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


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

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


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

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.05
p-value of test                       :    0.66

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

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.51
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    4.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :  120.47
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.94
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:51.52

Generator state:




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

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

MT19937


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


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

  j =  0                              :    1743165869845
  j =  1                              :        399908315
  j =  2                              :            45835
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.51

Generator state:




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

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

MT19937


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45509
p-value of test                       :    0.96


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

  j =  0                              :    1743165869509
  j =  1                              :        399908989
  j =  2                              :            45495
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

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

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


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

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


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

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


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

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

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

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

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

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


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

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

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

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




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

MT19937


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

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

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.24e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




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

MT19937


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


-----------------------------------------------
Normal statistic                      :   -2.90
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




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

MT19937


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


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




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

MT19937


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

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



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




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

MT19937


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

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



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:28.25

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

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

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

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

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

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




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

MT19937


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

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

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17679.20
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.69
p-value of test                       :    0.48


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.41
p-value of test                       :    0.28


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.49
p-value of test                       :    0.33


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.32
p-value of test                       :    0.16


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.93
p-value of test                       :    0.04


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.06
p-value of test                       :    0.63


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.06
p-value of test                       :    0.46


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.54
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.53
p-value of test                       :    0.50


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.37
p-value of test                       :    0.48


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.35
p-value of test                       :    0.18


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.57
p-value of test                       :    0.92


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.51
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.10
p-value of test                       :    0.97


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.09
p-value of test                       :    0.08


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.23
p-value of test                       :    0.88


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.22
p-value of test                       :    0.53


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.45
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.19
p-value of test                       :    0.86


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.86
p-value of test                       :    0.74


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.44
p-value of test                       :    0.05


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.09
p-value of test                       :    0.32


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.34
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.09
p-value of test                       :    0.09


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.58
p-value of test                       :    0.67


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.84
p-value of test                       :    0.61


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.18
p-value of test                       :    0.07


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.26
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




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

MT19937


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.11
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




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

MT19937


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.62

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

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

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

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

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.59
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




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

MT19937


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




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

MT19937


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

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

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




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

MT19937


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



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




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

MT19937


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



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




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

MT19937


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



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




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

MT19937


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



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

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




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

MT19937


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



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

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




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

MT19937


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




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

MT19937


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




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

MT19937


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




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

MT19937


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




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

MT19937


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.30
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000048724

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




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

MT19937


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.80
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999925307

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




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

MT19937


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:





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

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:34.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42991630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


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

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

MT19937


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:02:53.50

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

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

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

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

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.64

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

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

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.56

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:04:47.97

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

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

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.79

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

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

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.75

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

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

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.01

Generator state:




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

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

MT19937


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

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

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




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

MT19937


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


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

A2 test on the values of A2 (m-NP)    :    3.30
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


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

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


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

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




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

MT19937


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


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

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


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

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:36.86

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




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

MT19937


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


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

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

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

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

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    4.69
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :  118.85
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.62
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




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

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

MT19937


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:55.40

Generator state:




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

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

MT19937


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


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

  j =  0                              :    1743165869730
  j =  1                              :        399908547
  j =  2                              :            45716
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




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

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

MT19937


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


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

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


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

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

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


-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


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

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

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


-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


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

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




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

MT19937


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

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

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


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

Kolmogorov-Smirnov+ statistic = D+    : 5.87e-6
p-value of test                       : 1 -  5.9e-6    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

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

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

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

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

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

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




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

MT19937


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


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




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

MT19937


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


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




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

MT19937


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

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



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




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

MT19937


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

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



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:27.75

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




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

MT19937


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

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

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17377.65
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.93
p-value of test                       :    0.75


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.81
p-value of test                       :    0.30


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.98
p-value of test                       :    0.04


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.53
p-value of test                       :    0.33


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.47
p-value of test                       :    0.54


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.13
p-value of test                       :    0.19


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.89
p-value of test                       :    0.07


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.42
p-value of test                       :    0.55


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.84
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.40
p-value of test                       :    0.97


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.69
p-value of test                       :    0.30


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.72
p-value of test                       :    0.77


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.09
p-value of test                       :    0.98


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.01
p-value of test                       :    0.62


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.37
p-value of test                       :    0.50


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.59
p-value of test                       :    0.42


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.59
p-value of test                       :    0.9957


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.23
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.90
p-value of test                       :    0.95


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.93
p-value of test                       :    0.52


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.83
p-value of test                       :    0.83


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




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

MT19937


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.15
p-value of test                       :    0.19


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.13
p-value of test                       :    0.60


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5326.17
p-value of test                       :  6.9e-4    *****


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.59
p-value of test                       :    0.13


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.00
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




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

MT19937


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.18
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




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

MT19937


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




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

MT19937


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


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

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

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

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

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.83
p-value of test                       :    0.94

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



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




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

MT19937


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

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



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




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

MT19937


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


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

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

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

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

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

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

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

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




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

MT19937


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10343.91
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




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

MT19937


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



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




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

MT19937


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



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




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

MT19937


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



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




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

MT19937


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



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

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

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

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

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




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

MT19937


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



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

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

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

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




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

MT19937


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




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

MT19937


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




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

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12097.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.96
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999860618

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.93
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999971012

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:21.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 J (L=10000, r=15)   6.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43614222.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:37.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1518.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7182.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:51.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908149
  j =  2                              :            45918
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46187
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870187
  j =  1                              :        399907630
  j =  2                              :            46179
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17149.92
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.01
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.59
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.26
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.07
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.27
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5210.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.27
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.03
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.93
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.50
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.43
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12122.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.09
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999925493

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.49
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000061882

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:13.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44793870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.51
p-value of test                       :  5.5e-3

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.39
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.81
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908283
  j =  2                              :            45854
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908114
  j =  2                              :            45943
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.60
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.19
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.99
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.26
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.48
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.49
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.25
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4760.93
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.85
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.06
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.66
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9740.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.57
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999890486

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.28
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999944837

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:25.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45875214.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.33
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5258.23
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46159
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870159
  j =  1                              :        399907686
  j =  2                              :            46151
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908668
  j =  2                              :            45660
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.98e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17659.83
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.13
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.82
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.55
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.77
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.47
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.93
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.85
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.38
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.49
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 3.68e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.77
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.15
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000119155

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.21
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999979415

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:59.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46825486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.80
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:34.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.62
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.23
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908082
  j =  2                              :            45956
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908737
  j =  2                              :            45627
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.86e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17423.98
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   14.33
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.50
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.90
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.98
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.01
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.27
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.62
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.43
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.34
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.59
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000008083

Normal statistic for number of bits   :   0.064
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.22
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000053317

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:24.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47841294.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:10.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9906

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.12
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.14
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908425
  j =  2                              :            45783
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908130
  j =  2                              :            45929
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  3.1e-4    *****

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.48
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17194.87
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.85
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.95
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.58
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.23
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.13
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.98
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.18
p-value of test                       :  7.3e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999979934

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.70
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000134797

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:27.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48857102.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5551
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:37.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.57
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.82
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:59.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908222
  j =  2                              :            45886
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908583
  j =  2                              :            45704
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17956.04
p-value of test                       :  2.6e-3



-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.24
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.56
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.64
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.29
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.44
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.94
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.06
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.86
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9752.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:33.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.42
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000097054

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999931034

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:56.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49971214.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1494
p-value of test                       :  2.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334614
  j =  1                              :        599997012
  j =  2                              :             1494
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:37.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    3.17
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.39
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.72
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5226.10
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46254
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870254
  j =  1                              :        399907496
  j =  2                              :            46246
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908357
  j =  2                              :            45817
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:19.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.49
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.61
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.84
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.09
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.65
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.53
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.84
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.20
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.95
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.28
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.65
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.46
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.31
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.37
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999731138

Normal statistic for number of bits   :   -2.13
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.50
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999996044

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:10.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            2.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51019790.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9969

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.39
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.86
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.24
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46063
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870063
  j =  1                              :        399907878
  j =  2                              :            46055
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908518
  j =  2                              :            45735
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9907


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.14e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.98
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.74
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.11
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.66
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.38
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  300.91
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.46
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.53
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:29.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.65
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000116866

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.53
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999977549

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.60
p-value of test                       :  4.7e-3

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:02.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52068366.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.6e-3


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.28
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4829.29
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46185
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870185
  j =  1                              :        399907631
  j =  2                              :            46183
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908832
  j =  2                              :            45575
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:12.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17105.82
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.96
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.52
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.11
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.42
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5275.00
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.54
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.13
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.46
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:30.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4718.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.18
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.89
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.70
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.11
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000005011

Normal statistic for number of bits   :   0.040
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.37
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000155842

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:33.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53084174.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    3.45
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    4.04
p-value of test                       :  8.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.26
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.35
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:56.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46238
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870238
  j =  1                              :        399907528
  j =  2                              :            46230
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908508
  j =  2                              :            45740
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 3.95e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.49e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17816.45
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.91
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.21
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.51
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.90
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.24
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.64
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.21
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.95
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.77
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999999674

Normal statistic for number of bits   : -2.58e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.07
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999953879

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:15.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54132750.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.43
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.98
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.65
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45397
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869397
  j =  1                              :        399909209
  j =  2                              :            45391
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907923
  j =  2                              :            46034
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.18e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:18.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:19.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:12.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:12.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.27
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.43
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.57
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.85
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  297.68
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4795.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.15
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.53
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.22
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.37
p-value of test                       :  4.3e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.33
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9971

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:09.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:33.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11556.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.90
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000027241

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.55
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000038143

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:07.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 H (L=10000, r=0)    0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55181326.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1496
p-value of test                       :  2.3e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334616
  j =  1                              :        599997008
  j =  2                              :             1496
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1331.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.23
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.16
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.46
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46257
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870257
  j =  1                              :        399907489
  j =  2                              :            46251
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908547
  j =  2                              :            45722
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.28
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.80
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.99
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.51
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.66
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.29
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.12
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.28
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4693.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.38
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000101890

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.88
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999900191

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:47.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           2.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56229902.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5256.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908762
  j =  2                              :            45619
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907694
  j =  2                              :            46150
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.54
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.97
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.34
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.57
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.00
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.46
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.91
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.64
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.70
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10229.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.27
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999837785

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.94
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000133651

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:38.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57278478.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9929

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.93
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9918

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:15.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:29.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.42
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.58
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908668
  j =  2                              :            45663
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45412
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869412
  j =  1                              :        399909179
  j =  2                              :            45406
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.57
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.57
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.45
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.95
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.58
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.00
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.37
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:46.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.30
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.08
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999818501

Normal statistic for number of bits   :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.34
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999978899

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:16.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58327054.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:17.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  100.41
p-value of test                       :  8.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.14
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.76
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.02
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908221
  j =  2                              :            45888
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907841
  j =  2                              :            46075
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  4.6e-4    *****

Anderson-Darling statistic = A2       :    7.07
p-value of test                       :  3.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.03
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.96
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.72
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.55
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.70
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.06
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.92
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.11
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9762.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.37
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000041644

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.44
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999964892

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.96
p-value of test                       :  1.5e-3

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:35.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     8.4e-4
 46  MaxOft AD, t = 8                3.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59375630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7545
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7098
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:03:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:48.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6782.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.16
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.61
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908058
  j =  2                              :            45965
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907806
  j =  2                              :            46088
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.08
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17075.48
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.96
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.59
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.98
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.82
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.99
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.37
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.82
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.01
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.70
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.78
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.55
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999871280

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.11
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999909905

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:37.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60424206.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:49.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.82
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.72
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.15
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45462
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869462
  j =  1                              :        399909077
  j =  2                              :            45460
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908673
  j =  2                              :            45659
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.96
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.03
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.47
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.03
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.72
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.67
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.07
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.96
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.03
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.02
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000124774

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.78
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999935612

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:07.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61472782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:44.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:49.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.30
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908361
  j =  2                              :            45812
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46282
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870282
  j =  1                              :        399907438
  j =  2                              :            46278
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.73
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.59
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.21
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.32
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.19
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.65
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  454.39
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.08
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.40
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.32
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.77e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10350.18
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:08.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.74
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999947105

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.66
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000208204

Normal statistic for number of bits   :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:35.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62521358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    5.49
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.58
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    3.63
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1304.47
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.42
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4874.85
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908635
  j =  2                              :            45675
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908506
  j =  2                              :            45741
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.81
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:27.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17588.93
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.10
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.69
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.13
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.32
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.65
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.59
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.36
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.65
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.44
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12164.42
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.88
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000057721

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.66
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000135235

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.026
p-value of test                       :    0.51

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:09.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43024399.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7516
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:36.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.25
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.57
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908748
  j =  2                              :            45617
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908373
  j =  2                              :            45809
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.61e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:27.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:28.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.018
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.46
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.75
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  594.68
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.45
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.98
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.23
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.74e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9726.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.49
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.99
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999945413

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.20
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000098227

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:29.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 68  MatrixRank, L=1000, r=0         0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44335119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7514
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:19.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9911

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    3.08
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9936

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.48
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.50
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.24
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.77
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5229.30
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:22.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908397
  j =  2                              :            45800
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46464
p-value of test                       :  3.2e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870464
  j =  1                              :        399907076
  j =  2                              :            46456
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.92
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.84
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.10
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.47
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.90
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.63
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.29
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-2
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.35
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000025819

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.98
p-value of test                       :  4.5e-3


-----------------------------------------------
Total number of bits:  7999890909

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:32.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45187087.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1505
p-value of test                       :  9.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334625
  j =  1                              :        599996990
  j =  2                              :             1505
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.76
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5165.32
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908495
  j =  2                              :            45745
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908496
  j =  2                              :            45749
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.84e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.47e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.92
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.73
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.99
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.14
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.62
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.29
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.25
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.65
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.47
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.01
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.97
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.79
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.28
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000093004

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.68
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000116206

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:41.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.2e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46366735.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5589
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    4.06
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9969

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.01
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.86
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908383
  j =  2                              :            45804
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908203
  j =  2                              :            45894
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.41
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.94
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.33
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.26
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.20
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.22
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.94
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.95
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.54
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.13
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.37
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999934331

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.54
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999916772

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:56.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47415311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5581
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6710.93
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.36
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907617
  j =  2                              :            46184
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908106
  j =  2                              :            45944
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.26
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17377.36
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.04
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.16
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.97
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.48
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.02
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.44
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.70
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.25
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.14
p-value of test                       :  4.7e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10314.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.57
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999869171

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.42
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000024388

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:38.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48267279.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4838.84
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908698
  j =  2                              :            45642
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908690
  j =  2                              :            45652
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17744.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.04
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.61
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.58
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5263.56
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.72
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.59
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:38.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5121.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.01
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000137704

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.91
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000129499

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:15.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49512463.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9943


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.89
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1341.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4878.89
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908244
  j =  2                              :            45866
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908137
  j =  2                              :            45921
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    4.74
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.33e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17536.28
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.48
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.50
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.20
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.73
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.27
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.81
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.85
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.42
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3941.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11368.37
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12214.33
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.97
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000127681

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.69
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999956141

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:00.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50528271.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9921

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.07
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.85
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.02
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.66
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908183
  j =  2                              :            45895
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46115
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870115
  j =  1                              :        399907775
  j =  2                              :            46105
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9964


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 3.45e-4
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.35e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.72
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.70
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.09
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.19
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.98
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.92
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4775.58
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.05
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999955205

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.81
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999941039

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.49
p-value of test                       :  6.4e-3

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.99
p-value of test                       :  1.4e-3

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:06.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51511311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4470
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  369.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6880.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.65
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.54
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.75
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.83
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907717
  j =  2                              :            46140
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907736
  j =  2                              :            46126
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.95
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.29
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16879.37
p-value of test                       :    0.9985



-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.60
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.90
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.15
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.58
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.08
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.07
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.20
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000081724

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.97
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000040924

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:21.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52396047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    3.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.18
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7160.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4976.94
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908204
  j =  2                              :            45895
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907761
  j =  2                              :            46112
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.79
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.74
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.57
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.34
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.21
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.13
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.54
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.11
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.54
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000137365

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.75
p-value of test                       :  2.0e-3


-----------------------------------------------
Total number of bits:  7999999806

Normal statistic for number of bits   : -1.53e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:48.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53608463.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.83
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.57
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908342
  j =  2                              :            45823
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908608
  j =  2                              :            45690
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.44e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17719.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.86
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.51
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.80
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.13
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.39
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.25
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.72
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.84
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.80
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4310.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12128.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.74
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000060262

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.90
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000090580

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.032
p-value of test                       :    0.51

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:44.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54525967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5316
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7104
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:29.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.18
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.46
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908618
  j =  2                              :            45691
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908725
  j =  2                              :            45630
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.32
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.35
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.48
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.67
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.56
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.87
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.04
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.43
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.02
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10210.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9679.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4318.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.99
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000003856

Normal statistic for number of bits   :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.22
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999909080

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  7.0e-3

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:02.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55541775.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7112
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:19.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9958


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.57
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5165.84
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46144
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870144
  j =  1                              :        399907715
  j =  2                              :            46138
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908455
  j =  2                              :            45765
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.53e-6
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17261.56
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.37
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.71
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.13
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.40
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.53
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.54
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.35
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.71
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.50
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.20
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.40
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.24
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:30.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5003.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.90
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000051802

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.39
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000156445

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:03.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56623119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5316
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:46.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.40
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.69
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.55
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907883
  j =  2                              :            46057
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908034
  j =  2                              :            45977
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.06e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17162.85
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   68.06
p-value of test                       :  9.8e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.59
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.82
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.61
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   93.75
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.35
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.06
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.96
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.45
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.36
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.65
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3878.39
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.81
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999838262

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.36
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000028357

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:53.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 H (L=50, r=0)       9.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57671695.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.64
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4877.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908380
  j =  2                              :            45801
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907851
  j =  2                              :            46067
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.12e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.05
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.44
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.30
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.79
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.84
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.52
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.30
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:31.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.88
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12021.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.93
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000201457

Normal statistic for number of bits   :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.53
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999997736

Normal statistic for number of bits   :  -0.018
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:04.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58851343.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4117
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:17.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:47.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.15
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.85
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:57.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908110
  j =  2                              :            45939
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45541
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869541
  j =  1                              :        399908920
  j =  2                              :            45537
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.30
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17242.80
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.48
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.17
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.16
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.85
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.49
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.14
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.96
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.59
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.47
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.000
p-value of test                       :    0.50

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.21
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.90
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.79
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000025795

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.99
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000000892

Normal statistic for number of bits   : 7.05e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    2.52
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:11.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 14  BirthdaySpacings, t = 3         0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59867151.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.87
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.78
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908634
  j =  2                              :            45677
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908185
  j =  2                              :            45903
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.77
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.60
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.10
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.47
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.08
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.68
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.80
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.36
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.93
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.01
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.50
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.00
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000034747

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.44
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999865673

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:54.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61341711.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:47.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.57
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:28.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.94
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908225
  j =  2                              :            45880
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45496
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869496
  j =  1                              :        399909012
  j =  2                              :            45488
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.38
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.97
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.07
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.93
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.26
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.22
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.98
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.18
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.66
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.69
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.42
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.45e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.02
p-value of test                       :  7.1e-3

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4668.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.96
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.01
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000112510

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.49
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000023767

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:35.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62390287.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5238
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7554
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:47.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.78
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.26
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:46.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907670
  j =  2                              :            46159
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908056
  j =  2                              :            45966
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.04e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.98e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17363.87
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.24
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.34
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.45
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.46
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.44
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.50
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.65
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.28
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.22
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.10
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:21.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.63
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999926321

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.00
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000096343

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.7e-3

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         : 7.20e-3
p-value of test                       :    0.50

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:35.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63373327.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:22.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.34
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.58
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     117
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.17
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.64
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:52.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907811
  j =  2                              :            46090
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908848
  j =  2                              :            45567
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  1.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-6
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.62
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17165.12
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.93
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.27
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.25
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.75
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.32
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.34
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.55
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  474.11
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.37
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.27
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3932.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.30
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999858704

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.75
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999963134

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:37.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43057168.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7227.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.18
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.25
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4877.52
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:53.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908108
  j =  2                              :            45937
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908460
  j =  2                              :            45761
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17296.75
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.86
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.67
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5238.41
p-value of test                       :  9.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.10
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.94
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.81
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.53
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.78
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4326.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.31
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999915341

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.23
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000223963

Normal statistic for number of bits   :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.015
p-value of test                       :    0.51

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:49.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43646992.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:18.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:36.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.89
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907752
  j =  2                              :            46115
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908509
  j =  2                              :            45744
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.89
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.46
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.29
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4783.77
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.16
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.32
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.66
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999978683

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.22
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999792131

Normal statistic for number of bits   :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:01.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44662800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  510.89
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.22
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.78
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908594
  j =  2                              :            45703
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908666
  j =  2                              :            45664
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17676.47
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.92
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.35
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.17
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.24
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.25
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.13
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.12
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.14
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -401.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.02
p-value of test                       :    0.9954


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.32
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.63
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9957

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.35
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:32.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.99
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999919709

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.87
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000049405

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:56.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45744144.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5550
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    3.33
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.46
p-value of test                       :  5.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9981

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:35.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.01e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:47.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.25
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4843.41
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908507
  j =  2                              :            45745
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908076
  j =  2                              :            45959
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.08
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.68
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.89
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.52
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.22
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.34
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.99
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.18
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.70
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  147.33
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.60
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.91
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12042.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.18
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000040750

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.41
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000071305

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:48.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46956560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:37.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7085.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.56
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.47
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907782
  j =  2                              :            46106
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908529
  j =  2                              :            45734
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:27.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.35
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.26
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.25
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.95
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.45
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.37
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.71
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.01
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.31
p-value of test                       :  2.5e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.83
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.76
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:33.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.33
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.21
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999963281

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.36
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999986936

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  9.0e-3

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:59.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48398352.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.58
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.68
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.62
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908100
  j =  2                              :            45947
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907893
  j =  2                              :            46049
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.97
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.26
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.91
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.80
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.86
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.44
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.13
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.50
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.77
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000067324

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.83
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999947027

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:29.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49250320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.63
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.74
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:57.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908871
  j =  2                              :            45560
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908272
  j =  2                              :            45861
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   52.39
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.88
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.97
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.90
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.75
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.87
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.54
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.02
p-value of test                       :  5.5e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.74
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9725.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5121.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.00
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999941882

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.68
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000002968

Normal statistic for number of bits   :   0.023
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:17.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50364432.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.93
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    3.20
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.22
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.01
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.77
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907757
  j =  2                              :            46117
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908174
  j =  2                              :            45904
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.72
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.64
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.42
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.73
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.95
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.25
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.36
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  259.91
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.27
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.35
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.35
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999972947

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.56
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000098638

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:03.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51412993.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    3.97
p-value of test                       :  9.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.03
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.81
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.12
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.87
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.95
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908280
  j =  2                              :            45848
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45643
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869643
  j =  1                              :        399908717
  j =  2                              :            45637
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  9.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    6.32
p-value of test                       :  7.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.15
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.98
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.41
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  575.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.20
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.95
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.67
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.30
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.06
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.91
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9746.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.25
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000067888

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.50
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000005626

Normal statistic for number of bits   :   0.044
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:44.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft, t = 32                  0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52494337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:35.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.61
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:29.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.27
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:58.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908504
  j =  2                              :            45745
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.19
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  575.96
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.74
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.48
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.42
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.09
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.25
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.46
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:36.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12213.16
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.35
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999971153

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.23
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000003766

Normal statistic for number of bits   :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:00.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53510145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5311
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.04
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7219.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.75
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5183.26
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908331
  j =  2                              :            45830
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908120
  j =  2                              :            45937
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    6.55
p-value of test                       :  5.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.64
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.81
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.83
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.51
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.10
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.24
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.07e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.38
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.19
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999988067

Normal statistic for number of bits   :  -0.094
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.55
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000191866

Normal statistic for number of bits   :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:07.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               5.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54493206.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1479
p-value of test                       :  1.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334599
  j =  1                              :        599997042
  j =  2                              :             1479
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.15
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.83
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6865.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.79
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5183.67
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:57.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908161
  j =  2                              :            45915
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908028
  j =  2                              :            45983
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17587.32
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   65.57
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.71
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.48
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.14
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  258.13
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.67
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.26e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.37
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:35.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3933.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.81
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000032431

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.35
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000009124

Normal statistic for number of bits   :   0.072
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:01.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55607318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5220.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908486
  j =  2                              :            45754
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907961
  j =  2                              :            46018
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.28
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.67
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17780.43
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.01
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.27
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.94
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.97
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.81
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.05
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.00
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.46
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:35.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.71
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000114406

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.35
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999995528

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.088
p-value of test                       :    0.54

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56459286.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997127
  j =  2                              :             1435
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    3.04
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    3.43
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   89.60
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1341.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:30.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.03
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399907999
  j =  2                              :            45999
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908248
  j =  2                              :            45873
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17143.08
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.15
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.84
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.57
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.36
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.89
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.30
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.16
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.45
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.66
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.23
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.48
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:30.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4310.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.75
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999877550

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.05
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999932270

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:13.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57638934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5536
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.97
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7172.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.37
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5279.58
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908068
  j =  2                              :            45960
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45488
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869488
  j =  1                              :        399909028
  j =  2                              :            45480
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.70e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.40
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17767.95
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.75
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.98
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.13
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.88
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.68
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.54
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4816.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.81
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.44
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4782.97
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.97
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.98
p-value of test                       :    0.9957


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10366.70
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.60
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999898937

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.54
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000200452

Normal statistic for number of bits   :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58654742.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.23
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7137.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.52
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.02
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908754
  j =  2                              :            45620
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46281
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870281
  j =  1                              :        399907441
  j =  2                              :            46275
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.72
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.20
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.96
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.39
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.70
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.97
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.03
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:34.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.60
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999974411

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.66
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000070669

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:56.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59637782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7562
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.27
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46156
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870156
  j =  1                              :        399907693
  j =  2                              :            46146
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908094
  j =  2                              :            45947
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.056
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.79
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.17
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.70
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.23
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.20
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.20
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.88
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:35.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000075580

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.72
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000033679

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:45.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60686358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.59
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7242.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.10
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.23
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46251
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870251
  j =  1                              :        399907501
  j =  2                              :            46245
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45510
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869510
  j =  1                              :        399908982
  j =  2                              :            45506
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.16e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.10
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.28
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.27
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.94
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.80
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.99
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.20
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.68
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.84
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:30.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.54
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.22
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999885737

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.57
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999904223

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:02.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61734934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5319
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4541
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6814.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.11
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.56
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907922
  j =  2                              :            46036
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908916
  j =  2                              :            45536
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.63
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.82
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.04
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.89
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.41
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.73
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.21
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    2.89
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.09
p-value of test                       :  1.0e-2

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.87
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.68
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.14
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999978518

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.27
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000000061

Normal statistic for number of bits   : 4.82e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:16.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62717974.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:09.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1288.66
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.71
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.56
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908702
  j =  2                              :            45643
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46237
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870237
  j =  1                              :        399907530
  j =  2                              :            46229
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.03e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.72
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.92
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.25
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.12
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.05
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.37
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5153.89
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.02
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.76
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999894899

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.51
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999986543

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:27.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 85  Fourier3, r = 27                0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43089937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.15
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.89
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5263.97
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:57.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907772
  j =  2                              :            46102
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908643
  j =  2                              :            45674
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17564.34
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.60
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.50
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.60
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.85
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.27
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.77
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.18
p-value of test                       :  3.7e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.53
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.60
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.97
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000151990

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.83
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999935846

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :  -0.083
p-value of test                       :    0.53

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:44.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44040202.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     255
p-value of test                       :    0.9957

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:36.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  286.90
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.94
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908161
  j =  2                              :            45915
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908109
  j =  2                              :            45935
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.33
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   69.88
p-value of test                       :  8.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:27.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.65
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.66
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.64
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.71
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.53
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.05
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.67
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.49
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.12
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999959240

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.12
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000044539

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:28.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            8.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44924938.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7547
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.16
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.66
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.33
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.97
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908361
  j =  2                              :            45815
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907675
  j =  2                              :            46155
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.28e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.48
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.58
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.60
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.48
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.63
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.05
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.82
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.18
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.75
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.56
p-value of test                       :  4.6e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.28
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  7.8e-4    *****

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10304.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.34
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000015511

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.88
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999962165

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:45.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46301194.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    5.34
p-value of test                       :  2.0e-3

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.95
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.02
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.95
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46250
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870250
  j =  1                              :        399907502
  j =  2                              :            46246
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907708
  j =  2                              :            46140
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.68
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:27.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.85
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.92
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17574.45
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.75
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.22
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5278.07
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.58
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.94
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.21
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999994307

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.17
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999964097

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:48.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47218698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1333.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6769.09
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.46
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5181.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908337
  j =  2                              :            45821
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907720
  j =  2                              :            46137
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.90
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.98
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.99
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.23
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.67
p-value of test                       :  9.2e-3


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.88
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.87
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.67
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.47
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.41
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.71
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.08
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999907697

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.48
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999935153

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:42.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48103434.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    3.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.82
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.00
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.62
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907862
  j =  2                              :            46063
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907989
  j =  2                              :            46004
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17105.04
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.11
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.82
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.11
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.27
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.30
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.09
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.21
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.06
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999887549

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.08
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999917348

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.48

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:15.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49152010.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4788.75
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908773
  j =  2                              :            45606
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908185
  j =  2                              :            45897
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-5
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    : 3.44e-4
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17570.90
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.95
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.87
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.26
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.83
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.86
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3897.33
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.27
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000054511

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.18
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000074899

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:23.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50200586.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997253
  j =  2                              :             1372
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.09
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.02
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.25
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4810.12
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908384
  j =  2                              :            45808
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908119
  j =  2                              :            45933
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9982


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    5.68
p-value of test                       :  1.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.7e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.62
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17254.14
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.74
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.36
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.00
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.10
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.61
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.44
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.42
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.90
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.34
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.33
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999954479

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.07
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000072796

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:14.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft, t = 32                  2.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51281930.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.96
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     968
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    3.91
p-value of test                       :  9.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.60
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.47
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907828
  j =  2                              :            46080
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908313
  j =  2                              :            45842
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -3.13
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.82
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17206.97
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.05
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.75
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.86
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.96
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.20
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.50
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.67
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.39
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12049.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.30
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.51
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000024952

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.17
p-value of test                       :  9.8e-3


-----------------------------------------------
Total number of bits:  8000171046

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         : -1.24e-3
p-value of test                       :    0.50

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:23.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52461578.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.59
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.84
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908157
  j =  2                              :            45914
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908568
  j =  2                              :            45716
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.26
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17324.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  588.56
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.79
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.67
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.91
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.80
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.93
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.64
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.94
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999965000

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.04
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999964700

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:52.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53346314.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5676
p-value of test                       :  3.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.92
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.00
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:00.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908618
  j =  2                              :            45688
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907934
  j =  2                              :            46024
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.82
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.73
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.49
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.87
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.09
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.50
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.26
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.52
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  260.23
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4702.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.73
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000010681

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.12
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000085240

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:20.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         3.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54591498.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.97
p-value of test                       :  1.1e-3

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.39
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.80
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.58
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:06.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45481
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869481
  j =  1                              :        399909039
  j =  2                              :            45479
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45721
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869721
  j =  1                              :        399908565
  j =  2                              :            45707
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17607.01
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.32
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.74
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.44
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.59
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.68
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.66
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.42
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.83
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.27
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.16
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.67
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.26
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:32.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.11
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.87
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999993218

Normal statistic for number of bits   :  -0.054
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.03
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999965708

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         : 3.04e-3
p-value of test                       :    0.50

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:29.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55509002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    3.48
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:39.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.83
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.33
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869612
  j =  1                              :        399908778
  j =  2                              :            45608
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908307
  j =  2                              :            45845
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.50
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.36
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.22
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.08
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.47
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.69
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.36
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.22
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.27
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.32
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.39
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.32
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.47
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.73
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12093.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11585.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.79
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000002725

Normal statistic for number of bits   :   0.022
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.19
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000057256

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:59.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56655882.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.31
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  308.65
p-value of test                       :  5.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.33
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.06
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4895.23
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908378
  j =  2                              :            45808
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907936
  j =  2                              :            46026
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.40
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.95
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.94
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.96
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.23
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.31
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.60
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.61
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.88
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.60
p-value of test                       :    0.9997    *****

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:30.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.70
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000016831

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.40
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000010171

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:42.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      5.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57704458.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.80
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.11
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.39
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908633
  j =  2                              :            45682
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908418
  j =  2                              :            45785
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.12
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.15
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.75
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.14
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.67
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.05
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.66
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.86
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.40
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.33
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.04
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.29
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.30
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9587.64
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.32
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:30.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.88
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4342.96
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.59
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999948842

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999916628

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:52.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58621962.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   26.61
p-value of test                       :  3.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:49.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.88
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.22
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5375.80
p-value of test                       :  5.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908375
  j =  2                              :            45808
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908347
  j =  2                              :            45825
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.43
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.67
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.03
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.04
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.12
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.24
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.56
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.46
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.49
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.57
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.65
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.01
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000105742

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.28
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000110422

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.8e-3

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         : -5.80e-4
p-value of test                       :    0.50

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:31.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                3.9e-4
 42  Permutation, t = 7              5.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59703306.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5531
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.96
p-value of test                       :  9.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.82
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    3.13
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     366
p-value of test                       :  1.2e-4    *****

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  183.11
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.91
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.87
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908236
  j =  2                              :            45879
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907999
  j =  2                              :            45993
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.00
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.27
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.44
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.68
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.60
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.01
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.82
p-value of test                       :  5.3e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.17
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3886.80
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.27
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999994265

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.44
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999978032

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         : -4.80e-4
p-value of test                       :    0.50

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NJumps, t = 9        1.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60817418.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.76
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908701
  j =  2                              :            45645
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908013
  j =  2                              :            45989
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.20
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   65.80
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.82
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.06
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.87
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.34
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.27
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.60
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.96
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.29
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.68
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.27
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.98
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.11
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.85
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -403.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.46
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:36.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.70
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.49
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999983555

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.54
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000118627

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9957

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:11.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61931530.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5591
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:33.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    4.21
p-value of test                       :  6.9e-3

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.64
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.57
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.41
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.10
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908811
  j =  2                              :            45593
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907702
  j =  2                              :            46137
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  6.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.82
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.82
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.58
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.84
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.28
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.68
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.97
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -401.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.45
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.43
p-value of test                       :  1.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9597.69
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:22.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4672.97
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.02
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.96
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.59
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.01
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999939419

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.05
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000113677

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:04.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            5.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62947338.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.94
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.04
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.98
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:52.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908069
  j =  2                              :            45961
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907933
  j =  2                              :            46029
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.14e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:27.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:28.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.46
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.93
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.68
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.09
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.33
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.96
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.55
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -401.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.67
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.71
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10275.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5088.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11288.39
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.01
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999910367

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.70
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999870737

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:11.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 100  HammingIndep, L=1200, r=25      0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43122706.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.00
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.21
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5125.41
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908164
  j =  2                              :            45918
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.50
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.40
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.58
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.65
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.35
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.89
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.09
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.20
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.80
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4646.23
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.00
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999998270

Normal statistic for number of bits   :  -0.014
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.28
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000000964

Normal statistic for number of bits   : 7.62e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:52.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43810822.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  362.49
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6834.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.01
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:02:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:54.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907860
  j =  2                              :            46058
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908042
  j =  2                              :            45976
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.69
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.40
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.68
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.98
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.09
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.92
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.97
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.27
p-value of test                       :    0.9959

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  3.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.14
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4603.21
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.72
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000059596

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.55
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000071329

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:47.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44892166.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5569
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.92
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.02
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:52.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908334
  j =  2                              :            45824
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908244
  j =  2                              :            45875
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.01
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.10
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.27
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.98
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.08
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.83
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.88
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.76
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.85
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.08
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10209.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:48.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999996704

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.75
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000037636

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:21.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46071814.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4188
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    4.27
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.71
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:31.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.97
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.76
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:53.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45437
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869437
  j =  1                              :        399909129
  j =  2                              :            45431
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908405
  j =  2                              :            45793
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.95
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.26
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.24
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.51
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.51
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.06
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.40
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.23
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.73
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.36
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.75
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.97
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11363.30
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.56
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999885440

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.67
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999908156

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:06.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47153158.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.38
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  358.27
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6806.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.18
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.27
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907837
  j =  2                              :            46074
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907540
  j =  2                              :            46227
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.44
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.45
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.34
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.13
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.38
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.41
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.45
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.15
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.85
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.01
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999898421

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.95
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000031279

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48136198.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7118
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    4.54
p-value of test                       :  4.8e-3

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9974

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.88
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.95
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:59.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46217
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870217
  j =  1                              :        399907572
  j =  2                              :            46205
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908414
  j =  2                              :            45790
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.02
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.31
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.85
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.50
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.86
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.89
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.04
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.96
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.48
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.86
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999919571

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999821687

Normal statistic for number of bits   :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:50.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49020934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1500
p-value of test                       :  1.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334620
  j =  1                              :        599997000
  j =  2                              :             1500
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:37.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    3.17
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.83
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908360
  j =  2                              :            45814
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908471
  j =  2                              :            45757
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.93
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.99
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.16
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.55
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.49
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.66
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.53
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.12
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.39
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.32
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000095149

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.29
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999980063

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:00.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           1.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50003974.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4482
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    5.39
p-value of test                       :  1.9e-3

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.09
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.40
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.32
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46263
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870263
  j =  1                              :        399907480
  j =  2                              :            46251
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908652
  j =  2                              :            45671
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.00
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17472.55
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.20
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.67
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.19
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.34
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.74
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.35
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4294.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12115.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.00
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.97
p-value of test                       :    0.9950


-----------------------------------------------
Total number of bits:  8000083635

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.10
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000146245

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.29
p-value of test                       :    0.99

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:49.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51052550.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    4.63
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.47
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.96
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.42
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908137
  j =  2                              :            45924
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907852
  j =  2                              :            46068
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.80e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.64
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.39
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.06
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.22
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.66
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:31.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.74
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000006823

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.13
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999947558

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52101126.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.90
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908132
  j =  2                              :            45931
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908230
  j =  2                              :            45879
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.98
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-4
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:19.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:12.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.86
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.73
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.87
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.21
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.72
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.46
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -401.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.01
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.15e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9775.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:29.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4683.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5100.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.63
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999867182

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.08
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999930743

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:36.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53149702.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9912

Stat. AD after spacings (mNP2-S)      :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.85
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.87
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908174
  j =  2                              :            45907
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908646
  j =  2                              :            45671
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:12.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:12.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.64
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.79
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.46
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.23
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.82
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.50
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.06
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.46
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.76
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  1.0e-2

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:28.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.88
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11538.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000075001

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.71
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000128227

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:55.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54198278.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.23
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907950
  j =  2                              :            46016
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908354
  j =  2                              :            45817
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:18.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 3.11e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:12.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.52
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.32
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.13
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.06
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.47
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.91
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.76
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.25
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.93
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000029260

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.46
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000057220

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    2.68
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:57.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55246854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997341
  j =  2                              :             1328
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.46
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:10.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    3.48
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.38
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908621
  j =  2                              :            45685
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907675
  j =  2                              :            46152
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:18.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.82e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:19.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.29
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.35
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:28.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17421.61
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.34
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.18
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.05
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.30
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.07
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.88
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.20
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.62
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:28.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.08
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.23
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000089842

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.87
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999955526

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:14.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56295430.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1502
p-value of test                       :  1.3e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334622
  j =  1                              :        599996996
  j =  2                              :             1502
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.80
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.98
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908301
  j =  2                              :            45845
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908232
  j =  2                              :            45881
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:19.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:12.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:28.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:28.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17200.02
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.60
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.26
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.79
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.22
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.10
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.46
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.56
p-value of test                       :    0.9917

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12291.49
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999873482

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.41
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999979376

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:13.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            1.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57344006.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    3.10
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     539
p-value of test                       :    0.9939

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:37.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1332.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6861.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.53
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.28
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907988
  j =  2                              :            46000
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908342
  j =  2                              :            45820
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.57e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:30.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:29.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17329.07
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.95
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.30
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.72
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.51
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.99
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.24
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.81
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.86
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.44
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.30
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000007330

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.46
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999968591

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:16.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58359814.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7519
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.96
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.24
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:29.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.47
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.59
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908323
  j =  2                              :            45834
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908756
  j =  2                              :            45613
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :  8.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.87
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   46.25
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  399.39
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.27
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.71
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.64
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.01
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.26
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.63
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.42
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.34
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.84
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000053770

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.27
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999938759

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.21
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:33.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 J (L=1000, r=0)     0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59408390.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    4.75
p-value of test                       :  3.8e-3

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.71
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:45.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    6.49
p-value of test                       :  6.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   94.17
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.90
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.02
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908186
  j =  2                              :            45898
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908691
  j =  2                              :            45647
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.91
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.23
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.03
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.51
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.15
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.94
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.28
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.24
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.76
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.40
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.69
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.97
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12274.31
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.59
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999919625

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.98
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000065449

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:38.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60456966.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:46.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.33
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.82
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.60
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908427
  j =  2                              :            45782
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907930
  j =  2                              :            46032
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.65e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.06
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.27
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.63
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.29
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.79
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.77
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.73
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000044242

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.35
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999986237

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:46.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61505542.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:47.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.27
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7211.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.91
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5161.68
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908699
  j =  2                              :            45646
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907987
  j =  2                              :            46005
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.40
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.65
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.63
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.10
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.81
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.66
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.03
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.77
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.98
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.19
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12122.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.28
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000014749

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.77
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000046783

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.046
p-value of test                       :    0.48

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:42.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62554118.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4470
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    3.08
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.71
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.35
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.97
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.57
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908377
  j =  2                              :            45798
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.60
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.98
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.27
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.91
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  594.58
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.40
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.47
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.06
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.23
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.55
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.75
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.42
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000034636

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.45
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999898853

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:45.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43155475.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.88
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4886.58
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908476
  j =  2                              :            45759
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908827
  j =  2                              :            45582
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.89
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17628.49
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   70.23
p-value of test                       :  5.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.04
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.56
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.89
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.65
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.44
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:32.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.30
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.85
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.49
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11436.44
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.63
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999971042

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.74
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999909053

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:51.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 H (L=50, r=0)       5.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44466195.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:37.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.60
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.51
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45548
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869548
  j =  1                              :        399908909
  j =  2                              :            45538
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46294
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870294
  j =  1                              :        399907416
  j =  2                              :            46286
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.78
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.25
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.76
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.16
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.20
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.64
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.70
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.32
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9680.05
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9714.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.92
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999987437

Normal statistic for number of bits   :  -0.099
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.23
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000043552

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.34

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:55.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45285395.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.79
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    3.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.56
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.74
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.29
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.34
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908383
  j =  2                              :            45807
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908654
  j =  2                              :            45670
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.69
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17664.73
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.83
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.18
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.59
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.68
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.73
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5208.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.29
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4813.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.13
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.39
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :-1.40e-16
p-value of test                       :    0.50

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.37
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11588.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999965093

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.43
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000042772

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:27.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46268435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:33.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.20
p-value of test                       :  2.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9929

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.31
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.33
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.25
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908487
  j =  2                              :            45752
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45394
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869394
  j =  1                              :        399909218
  j =  2                              :            45382
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.75
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.57
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.55
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.89
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.52
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.24
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.98
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.46
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.23
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -403.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9997    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.79
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -5.14e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4645.04
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.53
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.68
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000147490

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.81
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000066952

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:06.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47087635.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:37.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.79
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.49
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.31
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7274.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.50
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.02
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.28
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908241
  j =  2                              :            45875
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908802
  j =  2                              :            45593
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.70e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.00
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.89
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.33
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.83
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.12
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5346.25
p-value of test                       :  3.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.46
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.37
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.52
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.90
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.33
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.37
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000030643

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000101992

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.63
p-value of test                       :  4.3e-3

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:06.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 J (L=10000, r=0)    3.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48332819.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.13
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907974
  j =  2                              :            46007
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908304
  j =  2                              :            45842
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17597.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.80
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.59
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.82
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.29
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.96
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.76
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.62
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.16
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.38e-5
p-value of test                       : 1 -  1.4e-5    *****

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.99
p-value of test                       :    0.9986

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.30
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.50
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000065374

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.50
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999884798

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:01.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49283091.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7542
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4849.38
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:07.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907744
  j =  2                              :            46125
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908793
  j =  2                              :            45596
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.72e-4
p-value of test                       :    0.9990    *****

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.00
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.3e-3

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.38
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   12.96
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.25
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.64
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.89
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.76
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.06
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.90
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.33
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4305.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.18
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000005278

Normal statistic for number of bits   :   0.042
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.72
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000200590

Normal statistic for number of bits   :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.70
p-value of test                       :    0.9965

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.74
p-value of test                       :  4.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.83
p-value of test                       :    0.9977

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:27.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 M (L=50, r=25)      0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50233363.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5522
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.35
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.54
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.18
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.75
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:08.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46399
p-value of test                       :  7.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870399
  j =  1                              :        399907203
  j =  2                              :            46397
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908357
  j =  2                              :            45814
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-5
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.12
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  425.63
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.32
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.05
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4814.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.51
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.51
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.25
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.95
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10348.50
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.03
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.99
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000014500

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.03
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000042097

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : -3.54e-3
p-value of test                       :    0.50

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:02.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51314707.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5297
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    3.36
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.84
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.53
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908086
  j =  2                              :            45954
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908655
  j =  2                              :            45668
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:28.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.18
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17266.38
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.82
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.07
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.23
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.78
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3945.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12130.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.11
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000094297

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.41
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000036826

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:44.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52330515.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4178
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.55
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    3.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.28
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.62
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.64
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907959
  j =  2                              :            46013
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908029
  j =  2                              :            45981
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.62e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.08
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17655.81
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.20
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.36
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.57
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.38
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.70
p-value of test                       :  2.2e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.34
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000079552

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.84
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999938528

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:09.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53444627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:18.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.41
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.33
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    3.25
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.32
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:30.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.84
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908698
  j =  2                              :            45645
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908001
  j =  2                              :            45995
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17531.23
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.88
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.88
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.70
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.38
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.45
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.89
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.46
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.82
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.91
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.18
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.86
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.15
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.57
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000154780

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.69
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000050779

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:41.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54394899.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.52
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.40
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.10
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.94
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908520
  j =  2                              :            45737
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908231
  j =  2                              :            45877
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.89e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.60
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.59
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.13
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.48
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.69
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.66
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.77
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.90
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.16
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.18
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.08
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9982

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.18
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4667.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.16
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.30
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000172207

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.50
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999946085

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:43.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55443475.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4168
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    3.27
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1331.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7234.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.88
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.66
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.51
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908658
  j =  2                              :            45662
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907904
  j =  2                              :            46045
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9906


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.11
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.89
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.54
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.75
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.99
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.61
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.88
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.93
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.50
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000035998

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.73
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000109813

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         : 3.22e-3
p-value of test                       :    0.50

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:49.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56492051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    5.26
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6880.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.66
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.83
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.29
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907853
  j =  2                              :            46072
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46301
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870301
  j =  1                              :        399907399
  j =  2                              :            46299
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  105.79
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17495.98
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.70
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.70
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.52
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.50
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.76
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.33
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.15
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4652.27
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.39
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999973343

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.23
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999857315

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:43.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57770003.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  498.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1338.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6993.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.36
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.70
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908526
  j =  2                              :            45734
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907603
  j =  2                              :            46194
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17775.56
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   66.26
p-value of test                       :  1.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.45
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.11
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.63
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.27
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.01
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4803.67
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.45
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.46
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.35
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.35
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5154.32
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.02
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999954311

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.84
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000060607

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:52.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58753043.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.05
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.81
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.68
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.52
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.88
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908270
  j =  2                              :            45856
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46180
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870180
  j =  1                              :        399907648
  j =  2                              :            46164
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.51
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.32
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.27
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.21
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.64
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.97
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.68
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.20
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.56
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.03
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.66
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.87
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9724.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:35.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11542.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.37
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000041089

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.06
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999885803

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:48.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59768845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:11.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.91
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.14
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:57.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46144
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870144
  j =  1                              :        399907713
  j =  2                              :            46142
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907789
  j =  2                              :            46101
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.99e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17044.14
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.21
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.84
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.42
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.54
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.02
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.05
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.31
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.68e-4
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.83
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.81
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.87
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.85
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999903377

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.28
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999862052

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:07.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60850189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7114
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.89
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.90
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.69
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:55.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908230
  j =  2                              :            45882
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46244
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870244
  j =  1                              :        399907517
  j =  2                              :            46234
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17236.78
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.61
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.22
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.52
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.57
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.88
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.28
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.34
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:36.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11556.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.30
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999994370

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.20
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999967520

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:39.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61865997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.26
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:34.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.50
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.21
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.12
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45552
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869552
  j =  1                              :        399908901
  j =  2                              :            45542
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907752
  j =  2                              :            46118
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9902


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.33
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.60
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.10
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.59
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.53
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.05
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.83
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4793.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.02
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.63
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.77e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.64
p-value of test                       :    0.9902

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:27.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9900

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.69
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999890837

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.76
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000193987

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:28.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62980109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     668
p-value of test                       :  3.3e-3

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.25
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.38
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.96
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907624
  j =  2                              :            46179
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907619
  j =  2                              :            46186
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17688.56
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.88
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.24
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.88
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.36
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.52
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.94
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  3.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9913

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9716.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.16
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000041419

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.66
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999929864

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:17.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43188244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:35.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  365.02
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6754.05
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.83
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:56.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908418
  j =  2                              :            45785
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908725
  j =  2                              :            45633
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 3.75e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.98
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.10
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17318.63
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.20
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.96
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.98
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.57
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.87
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.53
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.21
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999976940

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.34
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000122680

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:53.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43941908.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.08
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.30
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.55
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:53.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908259
  j =  2                              :            45863
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46319
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870319
  j =  1                              :        399907366
  j =  2                              :            46311
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.01e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.69
p-value of test                       :  1.6e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    6.55
p-value of test                       :  5.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   85.57
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.82
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.46
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.27
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.60
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.56
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.88
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.02
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5195.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.25
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.12
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.16
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11616.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.87
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000064228

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.01
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000083602

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:06.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44990484.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4501
p-value of test                       :  6.7e-3


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.28
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.07
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:51.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908779
  j =  2                              :            45603
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908079
  j =  2                              :            45950
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.01
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.68
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.064
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.05
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.25
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.77
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.95
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.19
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.08
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.33
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.33
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000073474

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.55
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999930338

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.026
p-value of test                       :    0.49

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:36.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45940736.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    4.47
p-value of test                       :  5.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1541.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5203.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45507
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869507
  j =  1                              :        399908987
  j =  2                              :            45505
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908337
  j =  2                              :            45830
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9941


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.91
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:27.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.45
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.10
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.52
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   87.94
p-value of test                       : 1 -  3.8e-5    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.16
p-value of test                       :  8.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.90
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.17
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.63
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.42
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.22
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.72
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000049375

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.25
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999950036

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:41.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)    1 -  3.8e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47054848.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4616
p-value of test                       :  1.4e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7095
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.86
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    3.73
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     970
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.27
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    3.70
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1324.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.69
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908445
  j =  2                              :            45773
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908916
  j =  2                              :            45536
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.48
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.31
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.15
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.86
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.86
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.22
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.16
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4796.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.13
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.25
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.62
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.34
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.73
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.48
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999675926

Normal statistic for number of bits   :   -2.56
p-value of test                       :    0.9948



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.31
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999995093

Normal statistic for number of bits   :  -0.039
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:39.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         1.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48201728.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5554
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.87
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:39.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.03
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:57.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908054
  j =  2                              :            45967
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907755
  j =  2                              :            46118
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.03e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.29
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.74
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.24
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.22
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.06
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.20
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.91
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.97
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.74
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999817490

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.56
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000068713

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:43.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49053696.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4174
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.87
p-value of test                       :  3.4e-3

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    3.93
p-value of test                       :  9.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     180
p-value of test                       :  9.4e-3

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6890.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.32
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:30.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.61
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4934.13
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908083
  j =  2                              :            45948
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908291
  j =  2                              :            45847
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17500.82
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.99
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.59
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.46
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.08
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.44
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.19
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.81
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.40
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4318.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.29
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000047656

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.43
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999985253

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.39
p-value of test                       :    0.9917

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:50.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50069504.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    2.72
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.93
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.39
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45115
p-value of test                       :    0.9998    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869115
  j =  1                              :        399909771
  j =  2                              :            45113
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908761
  j =  2                              :            45609
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    5.38
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.34
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.94
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.27
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.40
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.99
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.17
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.04
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4784.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.87
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.76
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.32
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10250.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12256.24
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.36
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000040990

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.33
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999909329

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:24.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51118080.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4183
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     541
p-value of test                       :    0.9923

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.94
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.01
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.21
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7199.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:29.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.25
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.12
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908581
  j =  2                              :            45699
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908353
  j =  2                              :            45819
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:14.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.53
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.96
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.44
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4830.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.00
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.56
p-value of test                       :    0.9901


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.29
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10235.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9670.73
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.12
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000003010

Normal statistic for number of bits   :   0.024
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.75
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999893921

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.21
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:48.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52756480.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.82
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.36
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.86
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:53.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45406
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869406
  j =  1                              :        399909190
  j =  2                              :            45402
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908288
  j =  2                              :            45850
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:11.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.14
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17720.84
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.04
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.57
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.35
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.47
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.21
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.88
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.77
p-value of test                       :    0.9970


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.83
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.16
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:38.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4689.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.57
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999947939

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000032677

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  8.9e-3

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:55.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53772288.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.00
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.88
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.81
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907988
  j =  2                              :            46003
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908220
  j =  2                              :            45884
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.67
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.70
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.91
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.72
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.27
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.72
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.25
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.46
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.82
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.22
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.79
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -403.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.31
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12087.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.41
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000059650

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.23
p-value of test                       :    0.9919


-----------------------------------------------
Total number of bits:  8000025663

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:36.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54788096.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.63
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  508.17
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.71
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908319
  j =  2                              :            45833
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908113
  j =  2                              :            45936
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.07e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.15
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.13
p-value of test                       :  8.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.07
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.20
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.35
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.35
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.54
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.10
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.52
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.40e-4
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.81
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5092.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.65
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000001477

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.55
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999953132

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55869440.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5327
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4483
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:20.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.30
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.14
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908124
  j =  2                              :            45932
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908515
  j =  2                              :            45732
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.21
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.25
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.27
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.80
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.82
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.36
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.80
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.08
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.83
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9753.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.09
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000043117

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.23
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000002860

Normal statistic for number of bits   :   0.023
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56918016.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5574
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    4.06
p-value of test                       :  8.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   26.74
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:30.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.92
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4912.31
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908325
  j =  2                              :            45833
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907810
  j =  2                              :            46089
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   18.08
p-value of test                       :  4.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17235.58
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.91
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.03
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.13
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.74
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.00
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.58
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.45
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.67
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.44
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000064906

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.78
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000010249

Normal statistic for number of bits   :   0.081
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:38.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 31  CouponCollector, r = 10         0.9993 
 68  MatrixRank, L=1000, r=0         4.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57966592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:26.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:21.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.62
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.97
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908238
  j =  2                              :            45869
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908175
  j =  2                              :            45908
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.26e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.98e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -2.82e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.033
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-4
p-value of test                       :    0.9990    *****

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17854.09
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.09
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.83
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4822.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.10
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4791.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.16
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.15
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.50
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.82
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10277.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.77
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:33.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4316.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11530.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.73
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000182716

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.51
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000011638

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:11.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58982400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.98
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.30
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.34
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.05
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4883.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908168
  j =  2                              :            45910
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399908000
  j =  2                              :            45994
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.11
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17245.44
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  393.05
p-value of test                       :    0.9999    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.70
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.59
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.45
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.87
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.84
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -403.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.31
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12124.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.45
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999896924

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.09
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000006526

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 J (L=1000, r=0)     0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60030976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:26.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.73
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.15
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  497.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.82
p-value of test                       :  1.8e-4    *****

Anderson-Darling statistic = A2       :    5.31
p-value of test                       :  2.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.21
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908246
  j =  2                              :            45871
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908383
  j =  2                              :            45804
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:09.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.38
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.78
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.81
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.87
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.55
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.67
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.24
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.07
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.18
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5090.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.59
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999973139

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.64
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000042952

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:52.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61112320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.81
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.55
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.83
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907970
  j =  2                              :            46006
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908114
  j =  2                              :            45940
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:09.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.80
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.76
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.17
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.10
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.78
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   14.88
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.08
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.28
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  579.66
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.33
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.34
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.33
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.79
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.14
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.35
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999931475

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.14
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000092245

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:57.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 H (L=50, r=25)      0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62128128.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:46.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:26.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.55
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.05
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.40
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908543
  j =  2                              :            45718
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908268
  j =  2                              :            45851
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :  1.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    8.11
p-value of test                       :  1.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   14.43
p-value of test                       : 1 -  6.7e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17596.26
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.92
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.45
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.43
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.39
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.27
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :-7.02e-17
p-value of test                       :    0.50

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.61
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.55
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:28.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000010237

Normal statistic for number of bits   :   0.081
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.21
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999925973

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:22.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0          1 -  6.7e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63176704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:18.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.06
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.17
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.77
p-value of test                       :  6.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.55
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   12.83
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.70
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.31
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.51
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45437
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869437
  j =  1                              :        399909130
  j =  2                              :            45429
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908252
  j =  2                              :            45871
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.46
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.88
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.66
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.94
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.20
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.61
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.36
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.01
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.65
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.81
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.53
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000065146

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.90
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000057127

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:52.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43221013.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.20
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908212
  j =  2                              :            45894
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45277
p-value of test                       :    0.9976


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869277
  j =  1                              :        399909451
  j =  2                              :            45267
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.44e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.17
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:27.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17056.50
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.51
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.75
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.51
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.20
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.61
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.19
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.22
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999894827

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.22
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999955172

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:45.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44269589.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:38.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.13
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907774
  j =  2                              :            46104
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907960
  j =  2                              :            46008
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:27.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:27.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17746.97
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.67
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.62
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.41
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.92
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.66
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.43
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -401.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.35
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.47
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000093958

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.44
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999892508

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:49.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45350933.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7571
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.40
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   44.28
p-value of test                       :  5.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.06
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.86
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.83
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5236.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908399
  j =  2                              :            45796
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907993
  j =  2                              :            46002
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  6.2e-4    *****

Anderson-Darling statistic = A2       :    6.47
p-value of test                       :  6.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.03
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.25
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.98
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.09
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  312.01
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.98
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.38
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.88
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.08
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.05
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10293.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3941.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.38
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.34
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999935312

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.21
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999872747

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.021
p-value of test                       :    0.51

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:54.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               5.3e-4
 52  SampleProd, t = 24              6.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46235669.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4840.43
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:55.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907723
  j =  2                              :            46134
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907897
  j =  2                              :            46044
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.08
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   68.72
p-value of test                       :  4.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.89
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.06
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.90
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  420.99
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.47
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.95
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.99
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.70
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.33
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.31
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.28
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.02
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.25
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.18
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.16
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000110107

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.63
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999979676

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.023
p-value of test                       :    0.51

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:40.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 65  SumCollector                    4.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47251477.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997261
  j =  2                              :             1368
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4102
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    4.07
p-value of test                       :  8.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     113
p-value of test                       :    0.9990    *****

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1330.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.32
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4934.83
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:56.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908043
  j =  2                              :            45974
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908611
  j =  2                              :            45687
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.39e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17098.91
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.86
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.73
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.59
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.23
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.31
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.46
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.02
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.78
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.49
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.56
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.84
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.87
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11563.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.21
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999940799

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.65
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999825293

Normal statistic for number of bits   :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:36.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         0.9998 
 25  ClosePairs NJumps, t = 16       0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48037909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9942

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.62
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908510
  j =  2                              :            45742
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908129
  j =  2                              :            45928
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17663.06
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.10
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.23
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.66
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.88
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.83
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.75
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.65
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.21
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.84
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999968444

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.61
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000148153

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:57.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49086485.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5311
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  367.75
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.32
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.72
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45538
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869538
  j =  1                              :        399908928
  j =  2                              :            45530
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908737
  j =  2                              :            45627
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 3.56e-4
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.89
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17729.57
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   14.45
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.00
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.60
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.39
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.57
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.78
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.81
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.02
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10247.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3933.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.05
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.77
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999936032

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.67
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000040060

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  9.0e-3

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:26.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 M (L=50, r=25)      0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50561045.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    3.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7252.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.64
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:21.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.70
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908826
  j =  2                              :            45572
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908035
  j =  2                              :            45981
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.00
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.25
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.23
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.60
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.84
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.63
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  583.54
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.36
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.40
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.79
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.18
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.94
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.88
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.62
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.05
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999976943

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.70
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999966869

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:24.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51707925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.97
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    4.14
p-value of test                       :  7.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:15.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.25
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.24
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.06
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908525
  j =  2                              :            45733
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908291
  j =  2                              :            45850
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.38e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.35
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.08
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   50.31
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.88
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.42
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   44.00
p-value of test                       :  3.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.07
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.34
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  132.76
p-value of test                       :  3.3e-5    *****


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5187.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.28
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.74
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.80
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    2.50
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.18
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.33
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12091.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12237.08
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.04
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000118918

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.61
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000112669

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.22
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      3.4e-4
 77  RandomWalk1 C (L=1000, r=20)    3.3e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52723733.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     179
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.56
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908483
  j =  2                              :            45754
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908169
  j =  2                              :            45911
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.42e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.78
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.69
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.39
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.68
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.78
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.92
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.92
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -401.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.28
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.89e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3938.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.48
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000091204

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.90
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999900188

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:40.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53805077.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4180
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:29.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907971
  j =  2                              :            46010
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907668
  j =  2                              :            46163
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9915


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.64
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.79
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.33
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.07
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.59
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.92e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9816.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.89
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999911252

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.20
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000171106

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.23
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:27.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54755349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:14.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7195.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.42
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:58.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46182
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870182
  j =  1                              :        399907638
  j =  2                              :            46178
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908515
  j =  2                              :            45738
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17363.44
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.76
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.75
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.32
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.42
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.83
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.11
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    2.49
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.50e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.73
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.60
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.59
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999971783

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.67
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999990761

Normal statistic for number of bits   :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:29.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55803925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7123
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.81
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.54
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908702
  j =  2                              :            45643
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908331
  j =  2                              :            45827
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.24e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-6
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.90
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.88
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.99
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.59
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.60
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.69
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.18
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.03
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.78
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.98
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.17
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.92
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999898955

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.92
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000148360

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56885269.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:34.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.55
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.67
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6836.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.71
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.91
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4753.84
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:56.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908202
  j =  2                              :            45896
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45577
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869577
  j =  1                              :        399908849
  j =  2                              :            45571
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17212.78
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.82
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.54
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.61
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  585.62
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.69
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.19
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.03
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4303.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.43
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.80
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999958748

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.37
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000055588

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:13.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57901077.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     824
p-value of test                       :    0.9946

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9922

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.64
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:54.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907905
  j =  2                              :            46040
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908355
  j =  2                              :            45815
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  5.4e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.91
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.37
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.46
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.18
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.08
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.47
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.64
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.93
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.00
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.88
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.14
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11468.90
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.55
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000058603

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.87
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999900266

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:48.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58884117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:35.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4478
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    3.67
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9921

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6849.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   21.55
p-value of test                       :  6.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.44
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4858.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:52.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908554
  j =  2                              :            45717
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908551
  j =  2                              :            45720
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.39
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.65
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.62
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.69
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.85
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.42
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.97
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.78
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.17e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.33
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:31.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.77
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000073639

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999993614

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:19.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 40  Permutation, t = 3              6.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59899925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    3.60
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:34.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:27.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.49
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.76
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.48
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:49.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908233
  j =  2                              :            45876
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908735
  j =  2                              :            45628
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-5
p-value of test                       : 1 -  1.2e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.33
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.26
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.63
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.09
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.35
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.29
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.99
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.37
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.01
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.13
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.32
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.49
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.64
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -401.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.49
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.69
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000061573

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.99
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999913472

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:13.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 85  Fourier3, r = 27                0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60948501.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.95
p-value of test                       :  9.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.37
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.86
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:55.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908655
  j =  2                              :            45671
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908434
  j =  2                              :            45777
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.06e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.63e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.93
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   48.28
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.19
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.81
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.34
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.85
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.89
p-value of test                       :  5.7e-3


-----------------------------------------------
Normal statistic for number of jumps  : -401.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.64
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.12e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.12
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.10
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.61
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000109396

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.35
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000120748

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:32.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61964309.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1234
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334354
  j =  1                              :        599997532
  j =  2                              :             1234
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9965

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.26
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:50.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46203
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870203
  j =  1                              :        399907596
  j =  2                              :            46199
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908364
  j =  2                              :            45812
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-4
p-value of test                       :  3.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 5.04e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    6.71
p-value of test                       :  4.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17121.14
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.50
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.89
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.90
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.30
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.95
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.72
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.92
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:22.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.02
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.80
p-value of test                       :  7.1e-3


-----------------------------------------------
Total number of bits:  8000116221

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.69
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000064186

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    2.90
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:48.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9998 
 54  SampleMean, r = 10              4.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62881813.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:19.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.08
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907882
  j =  2                              :            46056
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908341
  j =  2                              :            45825
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17795.77
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.04
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.61
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.86
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.11
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.55
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.95
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.35
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.56e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.87
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:31.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.72
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999989732

Normal statistic for number of bits   :  -0.081
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.59
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999977678

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:51.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43253782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    4.50
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:02:11.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.82
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.07
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.58
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908163
  j =  2                              :            45914
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908066
  j =  2                              :            45958
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.63
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.30
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.19
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.22
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.79
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.75
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.28
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.53
p-value of test                       :    0.9904


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.72
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.39
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.59
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999862355

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.24
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999893576

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:15.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43745302.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9941

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.98
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.88
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.02
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.26
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908567
  j =  2                              :            45706
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908651
  j =  2                              :            45670
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.18e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17080.58
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.21
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.28
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.98
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.31
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.75
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5214.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.84
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.95
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.97
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.38
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000015775

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.78
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999999833

Normal statistic for number of bits   : -1.32e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.058
p-value of test                       :    0.52

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:44.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44957718.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4156
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:36.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.68
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.37
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.18
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:53.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908730
  j =  2                              :            45632
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907791
  j =  2                              :            46100
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17549.11
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.56
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.44
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.13
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.02
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.57
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.16
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.96
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.62
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.08
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.56
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.85
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.80e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10307.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10260.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.05
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000073366

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.79
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000073783

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    2.69
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:36.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               7.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46137373.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997283
  j =  2                              :             1357
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.70
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:38.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.51
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:30.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.99
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908774
  j =  2                              :            45607
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907955
  j =  2                              :            46012
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.72
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.61
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   86.16
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17134.82
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.43
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.74
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  307.80
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.58
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.65
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.61
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.69
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.04
p-value of test                       :  7.0e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.96
p-value of test                       :    0.9985

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.45
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000059518

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.39
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999933443

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    2.43
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:00.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46989341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4206
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.51
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1339.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.34
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45631
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869631
  j =  1                              :        399908743
  j =  2                              :            45621
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908011
  j =  2                              :            45990
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.76e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.87
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.38
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.61
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.73
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.48
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9752.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.89
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000091777

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.36
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000204784

Normal statistic for number of bits   :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.04
p-value of test                       :  2.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.10
p-value of test                       :    0.9990    *****

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:18.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 105  AutoCor, d=1, r=27              0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48005149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  180.80
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.19
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:46.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908197
  j =  2                              :            45900
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45563
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869563
  j =  1                              :        399908877
  j =  2                              :            45557
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:15.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.80e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.22
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.90
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.68
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.89
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   93.65
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.98
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.85
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.70
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.85
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.60
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.73
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    2.59
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.89
p-value of test                       :  5.1e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4311.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11571.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.55
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000053632

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.75
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000188506

Normal statistic for number of bits   :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:43.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48988189.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.83
p-value of test                       :  3.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    5.75
p-value of test                       :  1.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     352
p-value of test                       :  1.8e-3

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.50
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7181.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.66
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5181.53
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908049
  j =  2                              :            45971
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908310
  j =  2                              :            45839
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.29
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:27.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   91.67
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.53
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.64
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.65
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.33
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.53
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.14
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.36
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.89e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.37
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9733.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.89
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000036964

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.18
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000106420

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:06.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50495517.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7532
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:29.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.34
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.93
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.02
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907953
  j =  2                              :            46016
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908253
  j =  2                              :            45869
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    : 3.63e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9983


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.14
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.36
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.80
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.73
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.40
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4761.34
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.24
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.73
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.90
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.31e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.28
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.09
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3943.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.61
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000107266

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.52
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000033991

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:29.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51478557.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5258
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    8.76
p-value of test                       :  5.4e-5    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    5.08
p-value of test                       :  2.6e-3

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:27.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.85
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.49
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  7.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.20
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:28.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.11
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.60
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.98
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.72
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.54
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.34
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.51
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.32e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.27
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.37
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.85
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999938087

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.14
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999986810

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:57.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            5.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52297757.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.12
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.41
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.85
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.64
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45455
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869455
  j =  1                              :        399909095
  j =  2                              :            45445
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907807
  j =  2                              :            46092
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9911


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17487.00
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.85
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.76
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.87
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.54
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.71
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.73
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.35
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.53
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.84
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.39
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.69e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.96
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10305.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12051.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.53
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000020770

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.84
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000005734

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:09.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53313565.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.82
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6903.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.48
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907852
  j =  2                              :            46065
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908121
  j =  2                              :            45932
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.46e-5
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17793.55
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.75
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.61
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.41
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.96
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.84
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.78
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.81
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.61
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999916001

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.41
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999860249

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.083
p-value of test                       :    0.47

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:44.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54624285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9959

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6855.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.12
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.92
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:47.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908483
  j =  2                              :            45757
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45557
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869557
  j =  1                              :        399908890
  j =  2                              :            45549
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.54e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.50
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.34
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.79
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.08
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.15
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.03
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.79
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.51
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.38
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.73
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.44
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.29
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.09
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.45
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.86
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.03
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.76
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.20
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.99
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.24
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999986780

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.37
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999980537

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:25.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55640093.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.88
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.05
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.12
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908599
  j =  2                              :            45696
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908408
  j =  2                              :            45796
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    4.07
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.30e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.82
p-value of test                       :  3.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16878.84
p-value of test                       :    0.9986



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.54
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.05
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.46
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.71
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.60
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.52
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.60
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.12
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:30.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.52
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999964232

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.00
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999998159

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    5.40
p-value of test                       :  2.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.87
p-value of test                       :    0.9979

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:24.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56557597.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1539.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.38
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:53.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908746
  j =  2                              :            45624
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45387
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869387
  j =  1                              :        399909228
  j =  2                              :            45383
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.82
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.11
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.92
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.64
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.14
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.34
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.77
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.77
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.29
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.78e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.51
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:29.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.08
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.52
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000002074

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.26
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999972686

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    2.45
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:04.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57540637.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9985


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.50
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9995    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1574.82
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6885.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.08
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.46
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907926
  j =  2                              :            46037
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907645
  j =  2                              :            46173
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   34.20
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.58
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.99
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.98
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.45
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.78
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.12
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.00
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  443.21
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.24
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.96
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.54
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10409.74
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.96e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9585.32
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.18
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000021628

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.24
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000032905

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:07.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         0.9995 
 59  WeightDistrib, r = 0            0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58556445.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.25
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907713
  j =  2                              :            46133
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908319
  j =  2                              :            45830
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.59
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.12
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17220.82
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.92
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.74
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.97
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.44
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.47
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.32
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.54
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9757.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:39.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.29
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999962279

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.20
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000112369

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:58.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59572253.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9927


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.11
p-value of test                       :  8.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.00
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.37
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.65
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.48
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908011
  j =  2                              :            45990
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908169
  j =  2                              :            45908
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.80e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17555.21
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.09
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.57
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.39
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.70
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.28
p-value of test                       :    0.9988


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.69
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.34
p-value of test                       :  9.7e-3

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.91
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.90
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:30.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.28
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999919685

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.91
p-value of test                       :  3.0e-3


-----------------------------------------------
Total number of bits:  7999782162

Normal statistic for number of bits   :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:06.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60620829.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1233
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334353
  j =  1                              :        599997534
  j =  2                              :             1233
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.16
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    5.05
p-value of test                       :  2.7e-3

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7235.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.39
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.64
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.65
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46282
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870282
  j =  1                              :        399907438
  j =  2                              :            46278
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908498
  j =  2                              :            45742
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.67
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  599.68
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.59
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.26
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.13
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.22
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.26
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.24
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.25
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.88
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.01
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.24
p-value of test                       :    0.01

Sample variance                       :    2.87
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.45
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.96
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:30.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.27
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999999626

Normal statistic for number of bits   : -2.96e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.43
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999963674

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:50.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9996 
 11  CollisionOver, t = 21           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61669405.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4178
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:45.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.24
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.26
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:56.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908444
  j =  2                              :            45769
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908249
  j =  2                              :            45865
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.33
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.60
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.35
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.29
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.17
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4803.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.54
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.15
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.00
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.24
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.45e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:26.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.88
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000185707

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.07
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000096967

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:48.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62783517.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:19.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9918

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.29
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45380
p-value of test                       :    0.9902


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869380
  j =  1                              :        399909240
  j =  2                              :            45380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908588
  j =  2                              :            45700
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.45
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.56
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.61
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.78
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.54
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.39
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.36
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.18
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.97
p-value of test                       :  1.5e-3

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10260.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.37
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000012667

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.43
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999952889

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:21.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43286551.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7649
p-value of test                       :  6.3e-5    *****


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.97
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:27.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.38
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908184
  j =  2                              :            45899
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.84e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -6.62e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.68
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.97
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.21
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.60
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.94
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.05
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.54
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.52
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.58
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.67
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    4.40
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10399.12
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.3e-3

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10349.60
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.99
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000055174

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.06
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999980627

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:28.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 18  BirthdaySpacings, t = 8         6.3e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44007441.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.13
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.70
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.62
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908214
  j =  2                              :            45884
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908533
  j =  2                              :            45729
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.04e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.81
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.32
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.57
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.19
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.16
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.56
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.69
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.79
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.50
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.99
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999958442

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.25
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999983549

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:15.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44859416.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    5.08
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9925

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6892.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.76
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.80
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:55.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46186
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870186
  j =  1                              :        399907631
  j =  2                              :            46180
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907619
  j =  2                              :            46177
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    8.50
p-value of test                       :  7.4e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  208.56
p-value of test                       :  1.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16887.45
p-value of test                       :    0.9983



-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.55
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.56
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.64
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.90
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.29
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.17
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.03
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :  1.5e-4    *****

Anderson-Darling statistic = A2       :    5.37
p-value of test                       :  2.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.89
p-value of test                       :  1.9e-3

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.33
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.69
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000135757

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000084535

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.21
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:26.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          1.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46170136.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:29.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:56.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   25.65
p-value of test                       :  5.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:28.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.69
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.27
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907840
  j =  2                              :            46074
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908464
  j =  2                              :            45759
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.19e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:14.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.91
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.62
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.22
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.79
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.91
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.09
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.97
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10231.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.69
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999827384

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.56
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999921293

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:54:07.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               5.8e-4
 53  SampleMean, r = 0               0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47317016.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4525
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.10
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.33
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4926.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908758
  j =  2                              :            45612
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908420
  j =  2                              :            45781
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.99
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9994    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.26
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.63
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.04
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.25
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.22
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5231.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.88
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.11
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.61
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.65
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999971090

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.36
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999956654

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:11.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48791576.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:48.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:28.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.05
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.59
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908114
  j =  2                              :            45934
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908223
  j =  2                              :            45887
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.64
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.34
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.61
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.88
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.98
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.89
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.77
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.82
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.55
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.93
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.41
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.50
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.10
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.79
p-value of test                       :  3.6e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.85
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:36.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.12
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999972233

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.50
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000137470

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  4.4e-4    *****

Anderson-Darling statistic = A2       :    8.01
p-value of test                       :  1.2e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.74
p-value of test                       :  9.3e-5    *****

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:26.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 105  AutoCor, d=1, r=27              9.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49807384.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    3.75
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     816
p-value of test                       :    0.9976

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9970

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:15.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:48.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.96
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:28.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.31
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.82
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907787
  j =  2                              :            46102
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908661
  j =  2                              :            45668
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:27.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.16
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.47
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.88
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  432.50
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.48
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.75
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.67
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.07
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.39
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.44
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000043381

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.30
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999798020

Normal statistic for number of bits   :   -1.60
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:03.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50790424.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    5.32
p-value of test                       :  2.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    4.06
p-value of test                       :  8.1e-3

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.56
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:46.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  171.14
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.09
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.82
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:28.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.31
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.06
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45537
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869537
  j =  1                              :        399908930
  j =  2                              :            45529
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908845
  j =  2                              :            45576
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.85
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17882.87
p-value of test                       :  8.0e-3



-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.36
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.94
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.05
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  415.55
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.82
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.90
p-value of test                       :  8.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.63
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.74
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.25
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:35.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.61
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000079645

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.96
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999736724

Normal statistic for number of bits   :   -2.08
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:25.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51904536.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    5.12
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.34
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:29.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.00
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.66
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:00.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908448
  j =  2                              :            45767
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.75e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17049.24
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.54
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.71
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.17
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.16
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.25
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.39
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.04
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 9.94e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4710.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.75
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000107767

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.39
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000059236

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:25.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52854808.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.57
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.60
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.10
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.79
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.39
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908813
  j =  2                              :            45589
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907483
  j =  2                              :            46254
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.84
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.05
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.78
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.24
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.59
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.21
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.01
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.58
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.35
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.76
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.41
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10225.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.15
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999848216

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.82
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000028816

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:27.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53903390.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7111
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7567
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:16.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.59
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.43
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.19
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908316
  j =  2                              :            45833
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:15.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:15.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.16
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.60
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.07
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.20
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.19
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.55
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.98
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.98
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.05
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:33.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.79
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000042667

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.26
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000053668

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    4.83
p-value of test                       :  3.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.00
p-value of test                       :  1.3e-3

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:19.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54951940.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4483
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.88
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:29.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.21
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.44
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908058
  j =  2                              :            45965
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46185
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870185
  j =  1                              :        399907633
  j =  2                              :            46179
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  108.09
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  108.00
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.18
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17125.23
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.80
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.22
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.16
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.19
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.45
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12256.41
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.82
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999996173

Normal statistic for number of bits   :  -0.030
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.00
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000068863

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.086
p-value of test                       :    0.47

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:58.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55902212.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.68
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1535.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.09
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.71
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908820
  j =  2                              :            45587
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907789
  j =  2                              :            46101
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.1e-4    *****

Anderson-Darling statistic = A2       :    6.17
p-value of test                       :  8.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.00e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.40
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17724.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.33
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.17
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.81
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.04
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.44
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.46
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.30
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.41
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.81
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.47
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999892415

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.50
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000044305

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:48.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16               8.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56950788.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.15
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1342.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:22.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.57
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.01
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45600
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869600
  j =  1                              :        399908804
  j =  2                              :            45592
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908582
  j =  2                              :            45706
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.50e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17682.17
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.82
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.60
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.31
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.59
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.71
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.44
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.24
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5233.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.61
p-value of test                       :    0.9907

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.2e-4    *****

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5094.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.81
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999988316

Normal statistic for number of bits   :  -0.092
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.51
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999835025

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:11.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57999364.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  184.87
p-value of test                       :  1.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.73
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908709
  j =  2                              :            45638
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908401
  j =  2                              :            45798
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.34e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.19
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.15
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.55
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.65
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.76
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.47
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:33.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.90
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.43
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000028294

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.42
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999900170

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:35.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 41  Permutation, t = 5              1.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59080708.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:45.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.08
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.44
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6812.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.41
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.94
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.80
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908358
  j =  2                              :            45818
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46145
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870145
  j =  1                              :        399907725
  j =  2                              :            46115
  j =  3                              :               15
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.67e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17318.94
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.90
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.52
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.25
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.18
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.51
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.16
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.57
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.88
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999903215

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.03
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999985715

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:45.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60129284.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:29.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.20
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.83
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908171
  j =  2                              :            45907
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45547
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869547
  j =  1                              :        399908910
  j =  2                              :            45539
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.85
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.39
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.90
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.51
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.99
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.86
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.62
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.19
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.04
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  8.9e-3

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.58
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.65
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11512.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.91
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000097408

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.64
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999988025

Normal statistic for number of bits   :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:04.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61145092.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.30
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.01
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.75
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45558
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869558
  j =  1                              :        399908888
  j =  2                              :            45550
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908095
  j =  2                              :            45951
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 3.32e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.42
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.00
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.80
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.64
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.75
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.33
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.36
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.18
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.53
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.86
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.45
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12114.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.97
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000098707

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.80
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999935159

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.6e-3

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:16.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62193668.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:19.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.28
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    3.13
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.50
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.28
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908542
  j =  2                              :            45726
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908444
  j =  2                              :            45769
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.33e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.78
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  172.53
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.20
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.62
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.62
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.88
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.63
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.49
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.25
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.90
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.64
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.70
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.26
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000043537

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.62
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000101539

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.035
p-value of test                       :    0.51

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:29.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63143940.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:48.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1479
p-value of test                       :  1.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334599
  j =  1                              :        599997042
  j =  2                              :             1479
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9908


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.11
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.28
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.63
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908666
  j =  2                              :            45658
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907754
  j =  2                              :            46117
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.47
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.98
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.79
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.12
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.25
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5195.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.12
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    2.43
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.00
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:37.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3893.63
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.05
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000006571

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.22
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000002209

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:40.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43319320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:28.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.28
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907836
  j =  2                              :            46073
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908598
  j =  2                              :            45695
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:27.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.88
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.06
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.32
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.60
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.10
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.31
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.96
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4792.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.83
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.77
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.98
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.14
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.98
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.03
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5136.81
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.77
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000020977

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.91
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999980027

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:07.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44236824.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.62
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4880.68
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907974
  j =  2                              :            46007
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    5.17
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.80
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.84
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.53
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.79
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.51
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.69
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  496.21
p-value of test                       :  9.4e-5    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.03
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.94
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.33
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:31.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.38
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.86
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12151.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.52
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000018463

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.01
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000039535

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:49.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   9.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44826641.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6761.35
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.87
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.64
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45290
p-value of test                       :    0.9971


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869290
  j =  1                              :        399909426
  j =  2                              :            45278
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908295
  j =  2                              :            45848
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:27.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:27.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17606.67
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.05
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.58
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.56
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.65
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.41
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.82
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.30
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.01
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999996833

Normal statistic for number of bits   :  -0.025
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.12
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000084634

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:47.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46432273.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7076
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9914

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.25
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.98
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908482
  j =  2                              :            45750
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908017
  j =  2                              :            45984
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.05e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.51e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.10
p-value of test                       :  9.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.23
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17669.89
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.54
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.04
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.75
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.93
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.41
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.16
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.70
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.10
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.68
p-value of test                       :  1.8e-5    *****

Anderson-Darling statistic = A2       :    7.98
p-value of test                       :  1.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5253.23
p-value of test                       :  1.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999971123

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.92
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999891263

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:40.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               9.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 96  HammingIndep, L=30, r=27        1.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47448081.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:28.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.71
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907980
  j =  2                              :            46001
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45681
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869681
  j =  1                              :        399908640
  j =  2                              :            45677
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    5.57
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.21
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.81
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.42
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.73
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.84
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.12
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.58
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.63
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  309.90
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.39
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.08e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9742.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.93
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000071362

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.86
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999942998

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Tests on the sum of all N observations
Standardized normal statistic         :  -0.025
p-value of test                       :    0.51

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:55.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48365585.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7284.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.01
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.24
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908516
  j =  2                              :            45736
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908449
  j =  2                              :            45768
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17148.29
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.73
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.15
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.95
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.15
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.51
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.94
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.27
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.30
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.12
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.90
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.79
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.38
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000010480

Normal statistic for number of bits   :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.93
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000181870

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:37.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49217553.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     116
p-value of test                       :    0.9977

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.97
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7326.28
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.06
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.20
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:51.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908733
  j =  2                              :            45626
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908125
  j =  2                              :            45924
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.99e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -3.16
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.02
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.68
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.61
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.04
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.79
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.24
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.18
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.97
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.60
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.36
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999987419

Normal statistic for number of bits   :  -0.099
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.83
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999850046

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:29.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50102289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    3.44
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.41
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1329.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.93
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.05
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908098
  j =  2                              :            45945
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45267
p-value of test                       :    0.9979


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869267
  j =  1                              :        399909468
  j =  2                              :            45263
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.41
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.38
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.59
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.61
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.34
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.76
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9775.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.35
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000105406

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.20
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999924794

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    2.50
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:34.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51216401.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.13
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5267.52
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46176
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870176
  j =  1                              :        399907651
  j =  2                              :            46170
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908413
  j =  2                              :            45789
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.51e-5
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.42
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.83
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.90
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.36
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.16
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.61
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5178.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.83
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.52
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.89
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.65
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000144607

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.64
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000013951

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:12.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52428817.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9955

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.49
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.35
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45561
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869561
  j =  1                              :        399908879
  j =  2                              :            45559
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908755
  j =  2                              :            45618
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17696.45
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.73
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.63
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.07
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.92
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.22
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.91
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.24
p-value of test                       :  9.5e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.48
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10224.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:32.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.64
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000013249

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.58
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000021559

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:19.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53215249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.20
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6860.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.24
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.93
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908170
  j =  2                              :            45912
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46282
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870282
  j =  1                              :        399907440
  j =  2                              :            46274
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.73e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17637.29
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.02
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.02
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.23
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.57
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.26
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.10
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.53
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.20
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.77
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.45
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.07
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:58.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9773.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.88
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.28
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000046615

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.99
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000095491

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    2.56
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:15.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54263825.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    6.36
p-value of test                       :  6.8e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.21
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6874.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.67
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.70
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5197.15
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:00.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908563
  j =  2                              :            45714
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46406
p-value of test                       :  7.1e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870406
  j =  1                              :        399907190
  j =  2                              :            46402
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.12
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.93
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.16
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.81
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.86
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  307.28
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.43
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.00
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.97
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:30.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4719.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5114.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000137533

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.92
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999974948

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:22.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          6.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55312401.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7114
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.90
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.65
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.49
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.54
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907670
  j =  2                              :            46159
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908404
  j =  2                              :            45795
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.89e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.06
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.17
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.55
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.51
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.77
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.41
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.48
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.59
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.92
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.85
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.72e-4
p-value of test                       :    0.9990    *****

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9648.24
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:29.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.05
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999953417

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999913508

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:29.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56328209.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4149
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    4.43
p-value of test                       :  5.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     981
p-value of test                       :  4.0e-3

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.59
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.71
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.46
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45772
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869772
  j =  1                              :        399908460
  j =  2                              :            45764
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908258
  j =  2                              :            45868
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17138.68
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.02
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.86
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.10
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.01
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.74
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5262.31
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.80
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.40
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.57
p-value of test                       :    0.9949

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.53
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.29
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000089329

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.70
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999977336

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:29.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57376785.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.39
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     256
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    3.88
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6779.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.17
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.25
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907823
  j =  2                              :            46075
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45382
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869382
  j =  1                              :        399909241
  j =  2                              :            45372
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.53e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    5.16
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.4e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:19.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.91e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.98
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17633.87
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.19
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.06
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.91
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.50
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.24
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.64
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.08
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.26
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.99
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.64
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999867869

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.56
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000112528

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft, t = 32                  5.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58425361.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1229
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334349
  j =  1                              :        599997542
  j =  2                              :             1229
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:22.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    3.62
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9915

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.67
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    5.68
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   12.74
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.23
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908321
  j =  2                              :            45835
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907730
  j =  2                              :            46132
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:18.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:12.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.90
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:29.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.96
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.63
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.38
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  411.51
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.19
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.10
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.07
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.77
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:30.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.16
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999967301

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.79
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999863855

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:08.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59473937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7174.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.61
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908472
  j =  2                              :            45755
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908146
  j =  2                              :            45924
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:19.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:19.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:12.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.19e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.59
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.81
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.15
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.17
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.52
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.16
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.22
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.14
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.78
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.95
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.42
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.71e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.18
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.09
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:29.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.51
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.18
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999933698

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.20
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999994052

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:47.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60522513.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:19.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:30.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5195.12
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908423
  j =  2                              :            45778
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908637
  j =  2                              :            45671
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:19.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:12.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:12.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:29.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.89
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.51
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.60
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.62
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  414.80
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.66
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.73
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.94
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.74
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.57
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.25
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.38
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.35
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:28.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.80
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999881261

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.49
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999978344

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:19.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61571089.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:36.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     662
p-value of test                       :  6.6e-3

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  376.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:20.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.83
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908894
  j =  2                              :            45547
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908070
  j =  2                              :            45962
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.89e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:18.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:12.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:12.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:29.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.71
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.74
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.81
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.86
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.53
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.08
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.60
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.42
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.88
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.70
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.20
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.23
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999907187

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.26
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000032617

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:36.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62619665.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    3.15
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.67
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6839.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.88
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.18
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908728
  j =  2                              :            45636
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45394
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869394
  j =  1                              :        399909218
  j =  2                              :            45382
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.46e-4
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.17
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.35
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.99
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.26
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.42
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.09
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.66
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.59
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5177.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.54
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.82
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.31
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10275.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.91
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.64
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000057481

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999983342

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    2.92
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:20.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43352089.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4189
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:29.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    4.24
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.99
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.16
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.23
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:59.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908505
  j =  2                              :            45743
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908498
  j =  2                              :            45745
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:20.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:15.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:15.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.73
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.69
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.75
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.97
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.11
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.79
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.21
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.92
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999934883

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.44
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000004981

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    2.57
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:54:33.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44072967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7141
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.22
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.58
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907953
  j =  2                              :            46016
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908607
  j =  2                              :            45689
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:12.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:14.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17715.37
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.78
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.18
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.85
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.85
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:46.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.61
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000049027

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.31
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000029158

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.19
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:30.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45613063.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:15.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.69
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907949
  j =  2                              :            46021
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908286
  j =  2                              :            45848
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.27e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:14.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.88
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.59
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.95
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.04
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5204.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.29
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.70
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.10
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.98
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.53
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.82
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.58
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:41.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12057.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12271.71
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.39
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999966935

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.56
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000063925

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:52.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46661639.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.12
p-value of test                       :    0.9998    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.65
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.63
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.20
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:29.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.63
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.92
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908028
  j =  2                              :            45980
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908552
  j =  2                              :            45718
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:14.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.64
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.69
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.66
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.16
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.97
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.09
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.92
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.94
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5249.30
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.68
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.92
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.15
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.72
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:40.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.00
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999922508

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.42
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999967259

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:06.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs NP, t = 5            0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47710215.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7056
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.96
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:28.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.37
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45269
p-value of test                       :    0.9978


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869269
  j =  1                              :        399909466
  j =  2                              :            45261
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907716
  j =  2                              :            46139
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.11
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17627.66
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.52
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.69
p-value of test                       :    0.9982


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.47
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.66
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.33
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.26
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.46
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.12
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.88
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000027979

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.48
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000008278

Normal statistic for number of bits   :   0.065
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:19.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48726023.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     544
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:46.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.85
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   74.61
p-value of test                       :    0.9995    *****


-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.44
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908379
  j =  2                              :            45806
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908299
  j =  2                              :            45846
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.92
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.50
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.60
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.04
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.09
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.89
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.35
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.27
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.22
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.09
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.61
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999896120

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.28
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999990077

Normal statistic for number of bits   :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.053
p-value of test                       :    0.48

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:45.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 41  Permutation, t = 5              0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49774599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   92.96
p-value of test                       :  7.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.47
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6793.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.60
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45569
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869569
  j =  1                              :        399908866
  j =  2                              :            45561
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908989
  j =  2                              :            45498
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.79e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.99
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17391.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.13
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.65
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.69
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.81
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.72
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.84
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.02
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.33
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.64
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.72
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.50e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.41
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.34
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10253.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.77
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999933056

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.24
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000012085

Normal statistic for number of bits   :   0.096
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:37.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          7.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50724871.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:47.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:28.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.66
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908764
  j =  2                              :            45612
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908824
  j =  2                              :            45585
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.93
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.89
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.81
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.57
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.64
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.88
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.58
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.52
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.91
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.16
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.03
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.44
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.70
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.52e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.67
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.74
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.36
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000030361

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.07
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000080800

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51838983.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  184.50
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7249.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.79
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.99
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45537
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869537
  j =  1                              :        399908930
  j =  2                              :            45529
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908212
  j =  2                              :            45888
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.3e-3


-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17297.29
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.94
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.41
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.43
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.03
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.43
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.39
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.68
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.61
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.11
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10280.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4680.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.41
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000015415

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.39
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000235495

Normal statistic for number of bits   :    1.86
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:01.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52920327.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4491
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.09
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.60
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908106
  j =  2                              :            45944
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908447
  j =  2                              :            45775
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.43
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.80
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17583.06
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.36
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.93
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.80
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.63
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.05
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.10
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.56
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.63
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.10
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.17
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.42
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.42
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.48e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.04
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9785.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.47
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.61
p-value of test                       :  3.2e-3


-----------------------------------------------
Total number of bits:  8000128881

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.17
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999869537

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:43.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53968903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9992    *****

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:12.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.66
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.76
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907723
  j =  2                              :            46131
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908131
  j =  2                              :            45930
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17901.12
p-value of test                       :  6.1e-3



-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.80
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.21
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.91
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.81
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.91
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.90
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.44
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999947438

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.04
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999986414

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         : 6.48e-3
p-value of test                       :    0.50

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:03.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55017479.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:36.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:50.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.20
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6831.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.34
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:56.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908241
  j =  2                              :            45878
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908262
  j =  2                              :            45863
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.65
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   51.15
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.61
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.76
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.66
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.72
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.09
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.50
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.73
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.02
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10256.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.54
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000107746

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.02
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000144217

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:56.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56098823.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.29
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:51.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.98
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907782
  j =  2                              :            46103
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908221
  j =  2                              :            45882
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:15.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 5.08e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.34
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.77
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.01
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  100.94
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.13
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.90
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.61
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.04
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.94
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.06
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.14
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.55
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:35.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.44
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999861896

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.91
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999887708

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:13.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57180167.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4493
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    3.10
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9914

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7274.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.59
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4865.88
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908573
  j =  2                              :            45697
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908184
  j =  2                              :            45896
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-5
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  9.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.73
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.96
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.77
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.95
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.66
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.64
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.68
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.25
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.51
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.89
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.76
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.72e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.03
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12163.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.42
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000089104

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.64
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000041086

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:58.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58195975.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:29.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.97
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7284.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.14
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.01
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4921.72
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908698
  j =  2                              :            45642
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908566
  j =  2                              :            45714
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.78e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.67
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.20
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.30
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.37
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.05
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.11
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.59
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.55
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.95
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.37
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.34
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12077.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.00
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999856343

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.01
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999884753

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:28.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 40  Permutation, t = 3              0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59277319.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7117
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:51.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.27
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.23
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.52
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:56.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907793
  j =  2                              :            46102
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907654
  j =  2                              :            46170
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.72e-4
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17156.31
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.19
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.91
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.11
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.76
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.21
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.56
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.35
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.78
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.77
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.31
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.31
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.36
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.83
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000019897

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.55
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999953198

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:58.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60325895.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.44
p-value of test                       :  5.5e-3

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:16.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:49.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:29.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4886.94
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907812
  j =  2                              :            46085
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45618
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869618
  j =  1                              :        399908767
  j =  2                              :            45612
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 4.26e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -1.89e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.67
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.39
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.09
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.09
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.74
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.95
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.74
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.07
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.39
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.01
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:37.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5160.41
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.00
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12151.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.57
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000091894

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.14
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999977312

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9921

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.047
p-value of test                       :    0.52

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:23.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61308935.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1225
p-value of test                       : 1 -  6.7e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334345
  j =  1                              :        599997550
  j =  2                              :             1225
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:48.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.34
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.73
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908736
  j =  2                              :            45626
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46379
p-value of test                       :  1.0e-2


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870379
  j =  1                              :        399907244
  j =  2                              :            46375
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  : 7.01e-3
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17566.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   37.83
p-value of test                       :  2.6e-3


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.46
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  148.06
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.06
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.93
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.07
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.78
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.25
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000058609

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999957812

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:52.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14          1 -  6.7e-5
 68  MatrixRank, L=1000, r=0         0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62357511.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7103
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.46
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.88
p-value of test                       :  1.0e-2

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5209.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:54.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907819
  j =  2                              :            46080
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908653
  j =  2                              :            45672
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.80e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.17
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.32
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.49
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.54
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.02
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.21
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.10
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:22.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.10e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4629.91
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.49
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999853370

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.32
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000028630

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:43.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63307783.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5554
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1554.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.67
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4871.01
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908000
  j =  2                              :            45997
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908582
  j =  2                              :            45700
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9901


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17658.11
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.11
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.86
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.46
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  274.02
p-value of test                       :  4.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.50
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.97
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.89
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10313.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.72
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000015775

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.99
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000068347

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:29.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    4.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43384858.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5616
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9996    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    4.24
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     654
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:10.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:38.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.52
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.83
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.14
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.54
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:55.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908338
  j =  2                              :            45828
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908120
  j =  2                              :            45928
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.02e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.96e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.53
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.51
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.56
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.64
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.86
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.94
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.20
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.27
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.65
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.29
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.79
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.90
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.90
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000003964

Normal statistic for number of bits   :   0.031
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.18
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999933212

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:07.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44204058.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     657
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.18
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.74
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:49.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907748
  j =  2                              :            46123
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907855
  j =  2                              :            46065
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.37
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.80
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.44
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.34
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.71
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.91
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.55
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.64
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.00
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.41
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.99
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.39
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000057286

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.86
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999974420

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:13.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44761114.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5280
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4479
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:14.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7236.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.68
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  163.33
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908479
  j =  2                              :            45759
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45576
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869576
  j =  1                              :        399908851
  j =  2                              :            45570
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17096.04
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.39
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.79
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.77
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.34
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.87
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.83
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.89
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.04
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.46
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.36
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.80e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.39
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4650.66
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3918.69
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.52
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999959243

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.56
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000058444

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:37.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45842458.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1490
p-value of test                       :  4.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334610
  j =  1                              :        599997020
  j =  2                              :             1490
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.39
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:35.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.99
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.90
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:54.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908167
  j =  2                              :            45909
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908814
  j =  2                              :            45587
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.81e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
p-value of test                       : 1 -  8.7e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17992.06
p-value of test                       :  1.4e-3



-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.39
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.80
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.13
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.44
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.45
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.86
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4801.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.91
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.07
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.89
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:33.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4696.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.52
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000019231

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.77
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000095557

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:09.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           4.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46858266.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.94
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.55
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907975
  j =  2                              :            46008
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908415
  j =  2                              :            45785
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-5
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.03
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.78
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.08
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.64
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.65
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.80
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.74
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.30
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.17
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.79
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.02
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9775.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12248.59
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.87
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999968759

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.14
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000015214

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.49
p-value of test                       :    0.9937

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:11.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47874074.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.11
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46296
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870296
  j =  1                              :        399907411
  j =  2                              :            46290
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908186
  j =  2                              :            45901
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17075.30
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.06
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.38
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.69
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.47
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.51
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.47
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.71
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9763.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4701.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.00
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000038482

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.18
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999971450

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:16.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48922650.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:36.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    3.66
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:44.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.62
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.00
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.91
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4895.53
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908541
  j =  2                              :            45722
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908597
  j =  2                              :            45697
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.21
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.90
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.72
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.97
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.06
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.34
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.20
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.53
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.88
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.00
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9733.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:27.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5111.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11423.14
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.35
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999965786

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.80
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999999977

Normal statistic for number of bits   : -1.82e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.045
p-value of test                       :    0.48

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:15.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49905690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.13
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   53.79
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.83
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.74
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.27
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907915
  j =  2                              :            46038
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907798
  j =  2                              :            46098
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  9.1e-3

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:12.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.60
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.24
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.00
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.07
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.17
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.61
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.62
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.93
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.16
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.42
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.54e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.49
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    5.75
p-value of test                       :  1.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10485.27
p-value of test                       :  3.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.56
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999930641

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.81
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000117799

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:15.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 90  HammingWeight2, r = 0           3.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50954266.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    4.55
p-value of test                       :  4.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     658
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.78
p-value of test                       :  4.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :   10.55
p-value of test                       :  7.9e-6    *****

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :    8.06
p-value of test                       : 1 -  2.2e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.25
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45539
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869539
  j =  1                              :        399908924
  j =  2                              :            45535
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908071
  j =  2                              :            45960
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:18.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:19.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.51
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.96
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.74
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.27
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.69
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.08
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.49
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.37
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.49
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.37
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.15
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.78
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.39
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.36
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:26.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5074.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.05
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999988226

Normal statistic for number of bits   :  -0.093
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.69
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999967529

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:06.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            8.6e-4
 38  Run, r = 0                     1 -  2.2e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52002842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5281
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    3.29
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   90.03
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  161.69
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908294
  j =  2                              :            45853
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908994
  j =  2                              :            45494
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:19.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   66.60
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.35
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.45
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.56
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.96
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.17
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.32
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.55
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.48
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.84
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.87
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:10.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:28.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.92
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.40
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000048004

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.99
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999945266

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:08.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53051418.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5258
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     835
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9923

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.25
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.44
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.18
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908434
  j =  2                              :            45777
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907896
  j =  2                              :            46046
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:19.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:12.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:28.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17249.62
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.75
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.84
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.05
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.02
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.46
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.44
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.09
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.89
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.18
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    2.83
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.99
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.17
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999929327

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.87
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000122599

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:43.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54099994.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5300
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4486
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7038
p-value of test                       :    0.9995    *****


-----------------------------------------------
CPU time used                    :  00:02:35.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:33.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:34.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908462
  j =  2                              :            45763
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908261
  j =  2                              :            45865
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:28.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.36
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.85
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.28
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.04
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.11
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.04
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.97
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:11.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:47.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5174.92
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.40
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.07
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000084253

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.25
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999902852

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:37.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 19  BirthdaySpacings, t = 8         0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55148570.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:35.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.02
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.79
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.07
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4941.20
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908363
  j =  2                              :            45817
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907914
  j =  2                              :            46040
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  8.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    4.92
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17814.84
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.71
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.75
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.21
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.06
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.02
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.10
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.84
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.75
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:44.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.22
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.97
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.05
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999944111

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.97
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000128197

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:01.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56197146.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5541
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.27
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.03
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.33
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908513
  j =  2                              :            45739
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908278
  j =  2                              :            45852
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:10.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17675.95
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.72
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.43
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.21
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.71
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.00
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.39
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.71
p-value of test                       :  5.7e-6    *****

Anderson-Darling statistic = A2       :    7.86
p-value of test                       :  1.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10469.83
p-value of test                       :  5.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.09
p-value of test                       :  8.2e-3


-----------------------------------------------
Total number of bits:  8000067189

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.16
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999984377

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:44.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 91  HammingWeight2, r = 27          5.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57245722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:29.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.14
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.97
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908638
  j =  2                              :            45672
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908550
  j =  2                              :            45719
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:10.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.96e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.42e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.31
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.44
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.60
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.27
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.67
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.75
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.17
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.73
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.44
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.05
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.22
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999990635

Normal statistic for number of bits   :  -0.074
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.66
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000048799

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.24
p-value of test                       :    0.01

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:08.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58294298.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     838
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.73
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:17.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:29.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.73
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908034
  j =  2                              :            45977
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908304
  j =  2                              :            45845
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.45e-4
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:19.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.74e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.00
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.69
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.11
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.70
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.08
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.00
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.05
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.42
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:31.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.96
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.03
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11505.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.61
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000019612

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.92
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999952073

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:27.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59342874.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:45.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6812.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.62
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:28.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.98
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4852.86
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46298
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870298
  j =  1                              :        399907408
  j =  2                              :            46290
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908554
  j =  2                              :            45717
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17507.33
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.06
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.50
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.94
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.38
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.20
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.14
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.60
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.81
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.82
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:03:27.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.68
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999941564

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.37
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000147061

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:54.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60391450.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.51
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.04
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1535.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.03
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:28.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908503
  j =  2                              :            45744
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908695
  j =  2                              :            45648
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:19.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17179.42
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.50
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.02
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.72
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.05
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.36
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.64
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.65
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.83e-4
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.36
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.66e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.25
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.42
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000062230

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.71
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000048172

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:16.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61440026.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    3.14
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.73
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1300.38
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6872.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.90
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46160
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870160
  j =  1                              :        399907684
  j =  2                              :            46152
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907605
  j =  2                              :            46190
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9964


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.89e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:12.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17524.36
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.29
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.31
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.33
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.39
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.12
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.14
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.01
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.20
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.00
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000135010

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.85
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999923174

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:14.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 85  Fourier3, r = 27                0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62488602.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    3.14
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5195.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908985
  j =  2                              :            45506
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908518
  j =  2                              :            45732
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17487.07
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.83
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.17
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.14
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.25
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.86
p-value of test                       :    0.9916


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.61
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.27
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.63
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.63
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.07
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -401.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.74e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.89
p-value of test                       :  5.1e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.98
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999910793

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.95
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000150232

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:11.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43417627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5559
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.10
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6849.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.37
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908178
  j =  2                              :            45905
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908650
  j =  2                              :            45669
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.07e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.41
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17112.43
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.12
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.40
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.99
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.85
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.21
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.01
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.51
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000034552

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.59
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000139363

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.36
p-value of test                       :    0.9908

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:10.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44433435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5319
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:30.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.57
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907917
  j =  2                              :            46034
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908071
  j =  2                              :            45957
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.01
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.56
p-value of test                       :  5.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.60
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.99
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.98
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.13
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.28
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.68
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.79
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.28
p-value of test                       :    0.01

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.04
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9720.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  6.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5169.80
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.50
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999884054

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.72
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999943244

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:54.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45449243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.17
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6887.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:29.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.85
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.63
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907932
  j =  2                              :            46025
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907892
  j =  2                              :            46048
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:10.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.17
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17000.40
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.29
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.47
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.24
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.15
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.71
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.46
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.91
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5195.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.53
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.58
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.48
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.02
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.20
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10319.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:45.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.04
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11518.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.31
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000054700

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.82
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000176971

Normal statistic for number of bits   :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:19.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46497819.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     656
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.97
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:45.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:20.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.13
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.42
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907890
  j =  2                              :            46049
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908136
  j =  2                              :            45926
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -8.20e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.99
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17418.45
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.62
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.61
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.42
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.10
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.82
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.45
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.03
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.05
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.49
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.60
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.93
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:35.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.46
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999996032

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.63
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999915779

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:43.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47644699.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:34.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7548
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    4.04
p-value of test                       :  8.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:09.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.80
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.25
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.76
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5161.11
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46450
p-value of test                       :  3.9e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870450
  j =  1                              :        399907103
  j =  2                              :            46444
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908454
  j =  2                              :            45770
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.04
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.91
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.82
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.72
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.58
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.23
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.99
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.98
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.43
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.31
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.72
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.70
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.91
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.14
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.73
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:35.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.81
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.62
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999975251

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.79
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999999893

Normal statistic for number of bits   : -8.46e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:24.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48562203.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    6.12
p-value of test                       :  8.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.09
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.27
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.96
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.02
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908138
  j =  2                              :            45928
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908170
  j =  2                              :            45915
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.07e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:27.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.79
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.77
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.84
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.04
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.49
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.52
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.38
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.62
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.90
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.28
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.67
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -401.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.07
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.09
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000029464

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.71
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999886439

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         : 7.26e-3
p-value of test                       :    0.50

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:47.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         8.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49643547.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997125
  j =  2                              :             1436
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.42
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:30.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.29
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4898.39
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908601
  j =  2                              :            45698
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908701
  j =  2                              :            45648
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17763.33
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.14
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.47
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.25
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.01
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.12
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.23
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.52
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.91
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.14
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.46
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3935.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.20
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000084787

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.90
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000107890

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:14.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50659355.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7085
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    5.00
p-value of test                       :  2.8e-3

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.87
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.55
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6764.65
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.78
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.38
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.77
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45581
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869581
  j =  1                              :        399908841
  j =  2                              :            45575
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46152
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870152
  j =  1                              :        399907697
  j =  2                              :            46150
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.23
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.57
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.67
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.38
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  145.94
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.19
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.04
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.88
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:34.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4269.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.00
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.36
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000106102

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.21
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000061807

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:44.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51642395.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7514
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.76
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.06
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.10
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.22
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45585
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869585
  j =  1                              :        399908832
  j =  2                              :            45581
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907742
  j =  2                              :            46126
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.55
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.15
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17240.22
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  183.89
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.07
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.51
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.59
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.53
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.16
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.65
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.57
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.22
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.86e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.12
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.85
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000031099

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.33
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000043000

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:03.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52658203.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997225
  j =  2                              :             1386
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4144
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    5.67
p-value of test                       :  1.4e-3

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7229.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.57
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5230.15
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:54.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908156
  j =  2                              :            45916
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46145
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870145
  j =  1                              :        399907715
  j =  2                              :            46135
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.64
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.16
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.96
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.70
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.76
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.87
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.60
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.19
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.94
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.31
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -401.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.50
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.97
p-value of test                       :  7.2e-3

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9707.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5110.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999934739

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.34
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999981785

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:35.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53674011.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     344
p-value of test                       :  6.9e-3

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    7.17
p-value of test                       :  2.9e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     112
p-value of test                       :    0.9993    *****

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.65
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.12
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.81
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908217
  j =  2                              :            45887
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908743
  j =  2                              :            45624
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 3.30e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17318.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.95
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.82
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.12
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.82
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.27
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.44
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999997802

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.36
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999882413

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:04.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         2.9e-4
 25  ClosePairs NJumps, t = 16       0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54657051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7540
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.70
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.75
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908212
  j =  2                              :            45888
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.16
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.20
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.69
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.81
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.24
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.18
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.80
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.88
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.79
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.32
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.11
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.69
p-value of test                       :  3.8e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.35
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10359.65
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:31.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.66
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999930047

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.57
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999823400

Normal statistic for number of bits   :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:33.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55476251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5273
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:39.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.08
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.95
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45439
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869439
  j =  1                              :        399909127
  j =  2                              :            45429
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908200
  j =  2                              :            45900
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.98
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17089.40
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.04
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.08
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.96
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5249.84
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10316.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:31.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11531.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.69
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.79
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000170194

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.29
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000035260

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.07
p-value of test                       :    0.02

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:42.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56426523.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:22.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.31
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.97
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.75
p-value of test                       :  9.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   11.95
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.90
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908618
  j =  2                              :            45685
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908660
  j =  2                              :            45664
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.30
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.28
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.39
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.18
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.43
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.11
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.06
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.06
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.17
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.39
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.95e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9612.43
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:29.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12102.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.50
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000140395

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.06
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  7999966101

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57475083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:29.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.95
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.27
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.86
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45522
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869522
  j =  1                              :        399908961
  j =  2                              :            45512
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907934
  j =  2                              :            46030
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.24
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.89
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.48
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.90
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.37
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.67
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.46
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.54
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.57
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.04
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999899162

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.56
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000096865

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:44.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58490891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7046
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.22
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6932.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.52
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907537
  j =  2                              :            46227
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908683
  j =  2                              :            45654
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.68
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.52
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.02
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.57
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.64
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.65
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.16
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.21
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.78
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.17
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.05
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.13
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000020959

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.55
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000114271

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         : -8.48e-3
p-value of test                       :    0.50

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:31.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59932683.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997303
  j =  2                              :             1347
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.24
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.41
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4898.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908572
  j =  2                              :            45708
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45487
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869487
  j =  1                              :        399909030
  j =  2                              :            45479
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.83e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:29.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.77
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.62
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.73
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.36
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.43
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.34
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.47
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.59
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    4.93
p-value of test                       :  3.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9579.22
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.79
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999937115

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.66
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999912902

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:39.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61014027.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.81
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.83
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  154.51
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.68
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:48.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908053
  j =  2                              :            45969
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908837
  j =  2                              :            45574
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   10.95
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.54
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   65.57
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.29
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.05
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.49
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.86
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.18
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.44
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.09
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5153.75
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.88
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4331.05
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.69
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000050119

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.34
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999943712

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:42.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           5.4e-4
 65  SumCollector                    0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62029835.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    3.72
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.85
p-value of test                       :  3.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    5.08
p-value of test                       :  2.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.55
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7224.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.55
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.85
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908534
  j =  2                              :            45730
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908766
  j =  2                              :            45608
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17192.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.40
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.85
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.38
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.85
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.30
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.34
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.79
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.61
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.90
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.76
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.98
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.26e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:22.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4688.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.17
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.54
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999917537

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.83
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999963221

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:45.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63045643.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.43
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7240.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.23
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5224.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:53.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908470
  j =  2                              :            45756
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46330
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870330
  j =  1                              :        399907344
  j =  2                              :            46322
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.53e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.19
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  172.64
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17225.11
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.19
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.92
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.41
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5210.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.24
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.76
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.26
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.32
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999918581

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.74
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999949760

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:13.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43450396.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:19.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9974

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    6.19
p-value of test                       :  8.1e-4    *****

Stat. AD after spacings (mNP2-S)      :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.69
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.07
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.80
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908327
  j =  2                              :            45835
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45573
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869573
  j =  1                              :        399908859
  j =  2                              :            45563
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.66
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.63
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.21
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.84
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.41
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.52
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.49
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.25
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.13
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.01
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.74
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.97
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9725.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.82
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000146224

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.20
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999923807

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:56.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         8.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43974679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1229
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334349
  j =  1                              :        599997542
  j =  2                              :             1229
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7555
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.33
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.74
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907704
  j =  2                              :            46133
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45292
p-value of test                       :    0.9970


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869292
  j =  1                              :        399909423
  j =  2                              :            45278
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.52
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.26
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.88
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.97
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  411.13
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.48
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.95
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.17
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.03
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.05
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.18
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.61
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.60
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.37
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4348.68
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.28
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000009802

Normal statistic for number of bits   :   0.077
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.93
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999929975

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:07.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45088791.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:18.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    3.02
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.10
p-value of test                       :  8.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.04
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:02:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.70
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.88
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:02:54.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907687
  j =  2                              :            46152
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908204
  j =  2                              :            45892
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.59
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.44
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.98
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.81
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.21
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.37
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.10
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.67
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.30
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000102613

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.84
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999941498

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:16.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46006295.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.11
p-value of test                       :  7.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9957

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.63
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.05
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907965
  j =  2                              :            46013
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46234
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870234
  j =  1                              :        399907537
  j =  2                              :            46224
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.020
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.39
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.69
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.25
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.38
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.31
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.36
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.91
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.70
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000025762

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.39
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999897248

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.34
p-value of test                       :    0.9902

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:39.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47022103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:37.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1325.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6896.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.24
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.48
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908732
  j =  2                              :            45631
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908083
  j =  2                              :            45954
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.98e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  105.41
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.16
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.78
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.96
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.41
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.90
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.06
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.60
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.09
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.62
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.66
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.30
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.89
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.31
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.52
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.85
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.15
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.36
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.12
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999897182

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.00
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000153286

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.21
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:03.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47972375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:34.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:28.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.23
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.70
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6688.87
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.40
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907911
  j =  2                              :            46040
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907734
  j =  2                              :            46127
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.14e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.57
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.65
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.06
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.98
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.78
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.96
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.76
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.29
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11534.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.12
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999986276

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.49
p-value of test                       :  9.2e-3


-----------------------------------------------
Total number of bits:  7999977396

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:15.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49545239.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7099
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4165
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:16.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6870.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:28.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.92
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.27
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908630
  j =  2                              :            45679
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908059
  j =  2                              :            45963
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17572.95
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.84
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.42
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.85
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.58
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.82
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.75
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.37
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.23
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.07
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.44
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3882.22
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12138.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.43
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000079561

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.69
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000098206

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:41.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50888727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    3.44
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:14.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.62
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.31
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46210
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870210
  j =  1                              :        399907584
  j =  2                              :            46202
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908036
  j =  2                              :            45976
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.18e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.04
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.55
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.85
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    3.80
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.78
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.90
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:36.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.11
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999896216

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.64
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000129037

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    5.20
p-value of test                       :  2.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.92
p-value of test                       :  1.8e-3

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:49.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51937303.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.01
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:16.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.45
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:29.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.02
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908380
  j =  2                              :            45804
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46267
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870267
  j =  1                              :        399907468
  j =  2                              :            46263
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.63
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.55
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.14
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.60
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.31
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.36
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.62
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.32
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.22
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.40
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.16
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.71
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5087.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12101.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.82
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000153793

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.01
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999948341

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:22.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52887575.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:35.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7072
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.95
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.37
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.18
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.73
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908143
  j =  2                              :            45927
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907941
  j =  2                              :            46022
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.97e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   16.29
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.21
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.36
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.20
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.47
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.83
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.27
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.81
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.30
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.03
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.86
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.01
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.12e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.72
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.36
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000076279

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.85
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000097762

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.65
p-value of test                       :  6.6e-5    *****

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    5.40
p-value of test                       :  2.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.89
p-value of test                       :    0.9981

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:42.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53936151.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    5.15
p-value of test                       :  2.4e-3

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.56
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907883
  j =  2                              :            46054
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908200
  j =  2                              :            45897
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.49e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.47
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.29
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.32
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.00
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.89
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.75
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.66
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.93
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.49
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -401.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.16
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10220.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11506.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.87
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000100108

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.41
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999957371

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:44.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54886423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   35.91
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.15
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908824
  j =  2                              :            45585
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908291
  j =  2                              :            45847
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.44
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.68
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.82
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.06
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.51
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.76
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.17
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.65
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5108.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.05
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.23
p-value of test                       :    0.9937


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.29
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.79
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:32.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.94
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999995885

Normal statistic for number of bits   :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.00
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000044782

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:31.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55836695.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4179
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    3.20
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7185.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.22
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907948
  j =  2                              :            46023
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907674
  j =  2                              :            46157
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  130.33
p-value of test                       :  5.8e-6    *****

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   67.88
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17714.49
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.47
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.96
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.07
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.78
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.03
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:31.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.24
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.38
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.17
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.69
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999924428

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.28
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999988745

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:20.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 59  WeightDistrib, r = 0            5.8e-6
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56852503.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:34.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   40.78
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.48
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.51
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.81
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908116
  j =  2                              :            45942
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907890
  j =  2                              :            46043
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.08e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17210.87
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.49
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.00
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.79
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.38
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.89
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.11
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5226.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.66
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.46
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.69
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.20
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3905.20
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.29
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999951755

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.90
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999865778

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         : 9.42e-3
p-value of test                       :    0.50

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:50.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57835543.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.96
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9993    *****

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.97
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:30.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.42
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.46
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908312
  j =  2                              :            45841
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45571
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869571
  j =  1                              :        399908863
  j =  2                              :            45561
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.05e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.10
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.47
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.23
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.58
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.86
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.13
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.41
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.43
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.90e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:31.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5067.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    4.51
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.46
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999962540

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.64
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999744365

Normal statistic for number of bits   :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.026
p-value of test                       :    0.51

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:27.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2, t = 3          0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58818583.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    3.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:10.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.42
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5175.46
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908915
  j =  2                              :            45538
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46187
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870187
  j =  1                              :        399907630
  j =  2                              :            46179
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.51
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9978


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.69
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.74
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.35
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.51
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.28
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.95
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.46
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4700.38
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.81
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.92
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.40
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.41
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.03
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.46
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:30.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12388.55
p-value of test                       :  1.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.94
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000017002

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.02
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000010117

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:15.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 99  HammingIndep, L=1200, r=0       1.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59834391.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9996    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7213.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.43
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5284.93
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907989
  j =  2                              :            46001
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908434
  j =  2                              :            45777
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.62
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.66
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.67
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.56
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.07
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.95
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   42.00
p-value of test                       :  1.1e-3



-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:31.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12101.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.60
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000029242

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.99
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000015427

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:57.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60882967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:47.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7148
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:26.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    3.23
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     976
p-value of test                       :  6.4e-3

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.94
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.71
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.51
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908185
  j =  2                              :            45906
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907829
  j =  2                              :            46078
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    5.90
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   75.17
p-value of test                       :  6.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.54
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.07
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.70
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.56
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.37
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.18
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.31
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.82
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999992345

Normal statistic for number of bits   :  -0.061
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.47
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000037843

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:08.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           6.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61898775.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.70
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   39.06
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.84
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:16.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.75
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.54
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908255
  j =  2                              :            45868
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908745
  j =  2                              :            45620
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-6
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.47
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17193.79
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.78
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.09
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.70
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.31
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.18
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.77
p-value of test                       :    0.9970


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.33
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.82
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.42
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10312.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -5.96e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4655.52
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.33
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999897752

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.30
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000015814

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:05.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63406103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    4.40
p-value of test                       :  5.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     550
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.15
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:35.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.40
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.11
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:59.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908477
  j =  2                              :            45757
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908305
  j =  2                              :            45834
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:28.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.40
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.02
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.84
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.46
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.78
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.60
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.94
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.93
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.36
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.00
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000081871

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.94
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000085762

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:03.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43483165.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.95
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6859.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:29.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.67
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.79
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46145
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870145
  j =  1                              :        399907712
  j =  2                              :            46141
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908565
  j =  2                              :            45713
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:15.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:15.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:28.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.76
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.98
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.43
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.81
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.66
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.65
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.59
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.96
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.50
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.04
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:32.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.25
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000009949

Normal statistic for number of bits   :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.69
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000029764

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:23.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44367901.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7195.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.46
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908302
  j =  2                              :            45846
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908051
  j =  2                              :            45970
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17585.48
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.88
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   98.90
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.22
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.59
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.35
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.77
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.74
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.35
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9770.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.00
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000001996

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.94
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999958415

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:16.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45219869.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:35.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.94
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7024.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.08
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:55.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908682
  j =  2                              :            45653
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907965
  j =  2                              :            46016
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.27
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.48
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.14
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.41
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.20
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.22
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.80
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9616.74
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.54
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.21
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999909974

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.01
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999732578

Normal statistic for number of bits   :   -2.11
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:20.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46104598.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.08
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.91
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7182.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.22
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.64
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.32
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:56.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908171
  j =  2                              :            45907
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908551
  j =  2                              :            45714
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.53
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17740.34
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.51
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.92
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.33
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.62
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.32
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.09
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.55
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.71
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.37
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.02
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999971513

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   29.98
p-value of test                       :    0.9967


-----------------------------------------------
Total number of bits:  7999949166

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:06.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47185942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.11
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.66
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:53.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908125
  j =  2                              :            45933
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908349
  j =  2                              :            45821
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.07e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.46e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.60
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:28.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.33
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.16
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.92
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.83
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.73
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.33
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.04
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.06
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000011902

Normal statistic for number of bits   :   0.094
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.76
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000040879

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.015
p-value of test                       :    0.51

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:41.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48168982.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    4.74
p-value of test                       :  3.8e-3

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:39.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1312.38
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.00
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.45
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.70
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:48.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908480
  j =  2                              :            45751
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907946
  j =  2                              :            46021
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.92e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.91e-6
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.42
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.91
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.94
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.00
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.11
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.40
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.93
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.46
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.57
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.50
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.21
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.40
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:33.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3927.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11986.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.63
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999998765

Normal statistic for number of bits   : -9.76e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.97
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000079522

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:16.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49184790.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.03
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.16
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:49.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908436
  j =  2                              :            45782
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908565
  j =  2                              :            45716
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  3.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.86e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.19
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.34
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.55
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.62
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.26
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.76
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.41
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.93
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.50
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.53
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.95
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000018499

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.19
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999969299

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.20
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:35.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50266123.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.86
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.00
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.22
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:50.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908026
  j =  2                              :            45981
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908679
  j =  2                              :            45653
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.87
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.56
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.25
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.56
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.34
p-value of test                       :    0.9936


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.87
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.06
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.71
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.12
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.58
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.55
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9702.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:37.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.94
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999956060

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.75
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999911732

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:52.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51380235.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.92
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    3.93
p-value of test                       :  9.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     256
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    3.89
p-value of test                       :  9.8e-3

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.16
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.15
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.79
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.75
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:51.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45358
p-value of test                       :    0.9926


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869358
  j =  1                              :        399909292
  j =  2                              :            45342
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908107
  j =  2                              :            45942
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.37
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.72
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.68
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.73
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.85
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.93
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.40
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.98
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000017299

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.42
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000075049

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:42.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52363275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6833.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.89
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.79
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:47.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908204
  j =  2                              :            45886
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908536
  j =  2                              :            45729
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9949


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17318.78
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  423.19
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.16
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.37
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.58
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.42
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.01
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.58
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10212.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.52
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000021727

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.50
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000049705

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:11.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53477387.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.20
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.13
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:28.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.69
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.55
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.65
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:55.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45216
p-value of test                       :    0.9990    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869216
  j =  1                              :        399909569
  j =  2                              :            45214
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908425
  j =  2                              :            45780
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  105.58
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.35
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.68
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.67
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.48
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.29
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.82
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.55
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.80
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.21
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.44
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.93
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.73
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999938417

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.47
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999985145

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:47.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54329355.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4535
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.93
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908455
  j =  2                              :            45762
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45526
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869526
  j =  1                              :        399908952
  j =  2                              :            45518
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17297.93
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.41
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.76
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.68
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.29
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.68
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.87
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.97
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.67
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.83
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999982244

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.00
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999960176

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:04.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55345163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.41
p-value of test                       :  5.6e-3

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    4.20
p-value of test                       :  7.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    6.22
p-value of test                       :  7.8e-4    *****

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.82
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.00
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.45
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908028
  j =  2                              :            45980
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908347
  j =  2                              :            45813
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.53e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17822.08
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.65
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.05
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.29
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.26
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.59
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.30
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.08
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.71
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.59
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.16
p-value of test                       :  5.2e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.68
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.64
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.69
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.02
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999935495

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.63
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000147535

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:02.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          7.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56393739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4509
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.21
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   86.50
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45513
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869513
  j =  1                              :        399908978
  j =  2                              :            45505
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908579
  j =  2                              :            45700
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  5.2e-4    *****

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.07
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.48
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.10
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.93
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.97
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  186.26
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.63
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.15
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.52
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.23
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.53
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.60
p-value of test                       :    0.9978


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.31
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:30.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12151.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.56
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999928901

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.29
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000069238

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:51.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57507867.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.98
p-value of test                       :  9.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.01e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.97
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:54.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907960
  j =  2                              :            46014
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908287
  j =  2                              :            45849
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.71e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:27.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.19
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.55
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.19
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.66
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.13
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.83
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.97
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.35
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.63
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.73
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.26
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:31.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.01
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999915926

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.87
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999971720

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58589211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5521
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7054
p-value of test                       :    0.9990    *****


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.00
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.86
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5161.79
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45659
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869659
  j =  1                              :        399908689
  j =  2                              :            45645
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45509
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869509
  j =  1                              :        399908985
  j =  2                              :            45503
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.05
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17664.97
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.61
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.75
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.53
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.27
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  306.15
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.66
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.77
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.38
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.34
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.63
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.56
p-value of test                       :  5.2e-3

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 3.46e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:29.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.50
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999961694

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.21
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999978467

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.66
p-value of test                       :    0.9961

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:44.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59605019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.02
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.05
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.75
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907990
  j =  2                              :            46002
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908143
  j =  2                              :            45918
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-4
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    : 1.39e-5
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.16
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.18
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.20
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.70
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.21
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.13
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  470.06
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.27
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.80
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.31
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.55
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -401.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:30.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4313.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.88
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000073600

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.28
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999861662

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:26.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60653595.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    4.55
p-value of test                       :  4.7e-3

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    5.25
p-value of test                       :  2.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     118
p-value of test                       :    0.9961

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6804.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.39
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.45
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.44
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907962
  j =  2                              :            46010
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46433
p-value of test                       :  5.0e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870433
  j =  1                              :        399907138
  j =  2                              :            46425
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  103.73
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.39
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.89
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.15
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.24
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.76
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.21
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.76
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.58
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.88
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.09
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.18
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.55
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12089.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000150073

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.16
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999858650

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:52.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61702171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5576
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.12
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.95
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:51.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908207
  j =  2                              :            45889
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.67
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.18
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.57
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.59
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.25
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.31
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    2.67
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:23.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.96
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000007669

Normal statistic for number of bits   :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.98
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000010255

Normal statistic for number of bits   :   0.081
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.048
p-value of test                       :    0.48

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:46.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62750747.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:19.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.36
p-value of test                       :  2.0e-3

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.05
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.95
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:47.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908655
  j =  2                              :            45671
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908917
  j =  2                              :            45534
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   61.92
p-value of test                       :  3.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   14.36
p-value of test                       :  7.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17692.90
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.94
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.52
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.44
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.09
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.63
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.03
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.88
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.71
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9763.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:32.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.70
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999870497

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.24
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000075400

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:42.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 65  SumCollector                    3.5e-4
 71  MatrixRank, L=5000              7.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43515934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:34.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.30
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908055
  j =  2                              :            45971
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908585
  j =  2                              :            45700
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :  6.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    7.31
p-value of test                       :  2.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.74e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.44
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.29
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.89
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.57
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.57
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.65
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.39
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.23
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.54
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.35
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.84
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.75e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.74
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.94
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.79
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.78
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000013183

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.64
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999934061

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:34.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft, t = 32                  0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43679774.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  279.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.33
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.96
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5213.33
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908185
  j =  2                              :            45903
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46230
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870230
  j =  1                              :        399907544
  j =  2                              :            46222
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17631.26
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.40
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.65
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.93
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.63
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.52
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.56
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.68
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.54
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999969689

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.70
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999978044

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:43.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45121566.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.50
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     966
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.69
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.64
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.24
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908313
  j =  2                              :            45842
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45621
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869621
  j =  1                              :        399908763
  j =  2                              :            45611
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.16
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.86
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.78
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.43
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.90
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.48
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.20
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.21
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.49
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.03
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.51
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4686.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.81
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999912845

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.79
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000013102

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.59
p-value of test                       :    0.9952

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:34.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45907998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:26.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.32
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.60
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908062
  j =  2                              :            45960
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45410
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869410
  j =  1                              :        399909185
  j =  2                              :            45400
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:16.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.32e-5
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17109.96
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.11
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.57
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.57
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.56
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.43
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.28
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.88
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.44
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.95
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.91
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.93
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:10.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:36.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12097.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.53
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999907853

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.40
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000097837

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:12.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47382558.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.36
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.61
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6805.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.22
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.41
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5241.48
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908375
  j =  2                              :            45802
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908563
  j =  2                              :            45714
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17553.11
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.05
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.91
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  417.02
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.94
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.56
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  148.02
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.28
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.24
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4393.02
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12059.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.20
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999886643

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.09
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000080908

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:07.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48660510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:46.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:48.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     841
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    3.29
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7177.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.33
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908275
  j =  2                              :            45858
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908165
  j =  2                              :            45913
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -5.83e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17212.75
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.35
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.55
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5353.47
p-value of test                       :  2.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.75
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.32
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.75
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.31
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.88
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.71
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.28
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.9921

Anderson-Darling statistic = A2       :    4.47
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9595.35
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:36.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4310.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.76
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000053347

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.47
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000035443

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:32.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 J (L=10000, r=0)    2.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49709086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5559
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    3.72
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     106
p-value of test                       : 1 -  9.4e-5    *****

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.23
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.43
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.22
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5234.77
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907788
  j =  2                              :            46103
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908650
  j =  2                              :            45672
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.81e-4
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.02
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    4.76
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16945.53
p-value of test                       :    0.9955



-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   62.17
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.70
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.73
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.27
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.97
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.50
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.09
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.52
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.14
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.39
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.28
p-value of test                       :    0.9958

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  261.71
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.88
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999897002

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.06
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000094945

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:27.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16      1 -  9.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50823198.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:35.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    3.02
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:47.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.79
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.57
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.06
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907742
  j =  2                              :            46126
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908528
  j =  2                              :            45733
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9900

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:14.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.71
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.61
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.54
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.38
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.31
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.79
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.19
p-value of test                       :    0.9967

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.04
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999960275

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.85
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000047674

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         : 7.70e-3
p-value of test                       :    0.50

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:48.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51740680.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5534
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.09
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    4.30
p-value of test                       :  6.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     543
p-value of test                       :    0.9903

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.06
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:20.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.78
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.11
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9999    *****


-----------------------------------------------
CPU time used                    :  00:02:51.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907988
  j =  2                              :            46003
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908096
  j =  2                              :            45949
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:14.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.14
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.73
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.05
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.88
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.42
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.67
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.38
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.23
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.73
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.14
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000171397

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.66
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999978416

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:02.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 43  Permutation, t = 10             0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52789256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7087
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:18.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    4.45
p-value of test                       :  5.3e-3

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:15.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:47.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.14
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908423
  j =  2                              :            45784
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908403
  j =  2                              :            45794
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    5.11
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  8.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.06
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.27
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.73
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.70
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.68
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.61
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.57
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.48
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.53
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.94
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.89
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.63
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  2.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    6.24
p-value of test                       :  8.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9529.90
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.14
p-value of test                       :  5.4e-3


-----------------------------------------------
Total number of bits:  8000093175

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.74
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999892358

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:41.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 91  HammingWeight2, r = 27          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53739528.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:16.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.94
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.04
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5194.84
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907763
  j =  2                              :            46114
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908021
  j =  2                              :            45985
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.66
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.25
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.97
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.85
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.54
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.38
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.50
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.51
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.24
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.94
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.43
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.78
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.30
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4651.57
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.00
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999955655

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999879542

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.31
p-value of test                       :    0.01

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         : 4.62e-3
p-value of test                       :    0.50

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:53.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54919176.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:46.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  291.71
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1527.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.26
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908524
  j =  2                              :            45732
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908228
  j =  2                              :            45880
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.46
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17857.40
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.34
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.86
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.26
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.66
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.31
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.35
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.09
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12037.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.77
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999896339

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.07
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000043039

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:03.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56033288.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7358.78
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:20.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.66
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.78
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908367
  j =  2                              :            45812
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907906
  j =  2                              :            46041
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.67
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.92
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.15
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4777.60
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.76
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.52
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.76
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.48
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.14
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:32.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.48
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000084391

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.07
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000088801

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:59.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57081864.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997319
  j =  2                              :             1339
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    4.81
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:45.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.08
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.39
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.97
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908427
  j =  2                              :            45785
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908588
  j =  2                              :            45700
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.42
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17227.94
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.08
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.98
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.71
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.57
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.13
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.38
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12067.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.13
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000043621

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.00
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000085255

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:37.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58032136.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1253
p-value of test                       :    0.9988

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334373
  j =  1                              :        599997494
  j =  2                              :             1253
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    4.38
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.19
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.47
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.05
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:48.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908381
  j =  2                              :            45802
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908569
  j =  2                              :            45714
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.55
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.37
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.39
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.27
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.19
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5193.02
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.84
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.53
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.95
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000223585

Normal statistic for number of bits   :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.01
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999992897

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:44.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59015176.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    3.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.58
p-value of test                       :  1.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.15
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9943

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1323.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6840.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.53
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5109.71
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908506
  j =  2                              :            45741
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908455
  j =  2                              :            45771
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.0e-3


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.54
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.36
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.64
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.15
p-value of test                       :    0.9901


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.04
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.47
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.58
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.24
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.48
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.78
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.37
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999964400

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999869015

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:13.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59998216.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7512
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   95.54
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4921.42
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907926
  j =  2                              :            46034
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907899
  j =  2                              :            46049
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.43
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.47
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.66
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.37
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.10
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.80
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.26
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.26
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.38
p-value of test                       :  6.8e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   31.02
p-value of test                       :  2.0e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.32
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.39
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.90
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999986384

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.82
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000031774

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:03.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60915720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7505
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     674
p-value of test                       :  1.6e-3

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.52
p-value of test                       :  1.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.31
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:45.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:26.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.70
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:48.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908279
  j =  2                              :            45853
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908916
  j =  2                              :            45536
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17000.26
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.53
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.40
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.16
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.82
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.88
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.44
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.48
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.89
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.27
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.65
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.49e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.24
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -9.05e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.29
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999977915

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.17
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000006760

Normal statistic for number of bits   :   0.053
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:18.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61997064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.21
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.00
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.02
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907750
  j =  2                              :            46116
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908266
  j =  2                              :            45867
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.9900

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.46
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.26
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.63
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.82
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.82
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  600.48
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.36
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.54
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.87
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.71
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.73
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.46
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -401.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.59
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:23.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.68
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.52
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.40
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000015586

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.63
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999947312

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.41
p-value of test                       :    0.9920

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:29.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62914568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:29.12

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:24.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5559
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:34.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  365.27
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.27
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:29.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.03
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.74
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908553
  j =  2                              :            45716
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908512
  j =  2                              :            45741
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  1.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:14.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:15.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.84
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.81
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.53
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.66
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.66
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.76
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.91
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.04
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.29
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.05
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999889088

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.20
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999852164

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:53:32.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43548703.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:33.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.18
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.96
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.84
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.54
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.71
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908618
  j =  2                              :            45688
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.87e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.06
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.85
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.93
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.94
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.67
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.88
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.59
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.79
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.96
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.74
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9747.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:35.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.26
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999916283

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999992630

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :  -0.064
p-value of test                       :    0.53

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:11.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44531743.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997335
  j =  2                              :             1331
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9984


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:09.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.34
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.51
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45986
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869986
  j =  1                              :        399908036
  j =  2                              :            45970
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907741
  j =  2                              :            46128
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    4.35
p-value of test                       :  6.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:14.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    5.51
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   82.52
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.92
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.81
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.11
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.32
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.90
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.80
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.90
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.76
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.37
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.51
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.98
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.16
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.16
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.79
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10229.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5183.86
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.67
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999965138

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.12
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999929429

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:39.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45482015.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    3.02
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     827
p-value of test                       :    0.9927

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.22
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907694
  j =  2                              :            46150
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908258
  j =  2                              :            45865
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.51
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17706.29
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.97
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.69
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.32
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.43
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000014095

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.70
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000052576

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  2.6e-4    *****

Anderson-Darling statistic = A2       :    6.21
p-value of test                       :  8.4e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.12
p-value of test                       :  9.0e-4    *****

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:43.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            7.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 103  AutoCor, d=1, r=0               9.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46530591.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5288
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    4.17
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    5.52
p-value of test                       :  1.6e-3

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:30.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.26
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.78
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908184
  j =  2                              :            45902
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908037
  j =  2                              :            45977
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.05
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.05
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.80
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.53
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.21
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.14
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.38
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.50
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.36
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  6.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  267.34
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.95
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.03
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.97
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000146956

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.20
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999987254

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.84
p-value of test                       :    0.9978

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:57.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47513631.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    3.05
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     838
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.97
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.07
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4911.51
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:47.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908201
  j =  2                              :            45895
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908548
  j =  2                              :            45726
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  7.6e-4    *****

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  4.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17433.50
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.80
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.06
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.52
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.07
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.86
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.08
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  313.95
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.18
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.84
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.14
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.50e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.46
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10315.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.96
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000186535

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.73
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000028462

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:06.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48529439.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.02
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.55
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.16
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907981
  j =  2                              :            46005
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908587
  j =  2                              :            45702
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  6.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.17
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.44
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.02
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.64
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.81
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.48
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.88
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.79
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -8.20e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.05
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000121033

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.01
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000025138

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:48.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49479711.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:28.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:47.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.66
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.04
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.37
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.35
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:52.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908191
  j =  2                              :            45903
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908479
  j =  2                              :            45753
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.84
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5236.67
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.35
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.09
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.19
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.51
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.20
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.01
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.53
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    7.39
p-value of test                       :  2.4e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.17
p-value of test                       :    0.9992    *****

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12117.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12289.19
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.97
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999935093

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000001456

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.13
p-value of test                       :    0.02

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.65
p-value of test                       :  4.1e-3

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:09.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 83  LempelZiv, r = 15               0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50429983.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:16.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:50.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:28.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.74
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.31
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:00.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908384
  j =  2                              :            45805
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46121
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870121
  j =  1                              :        399907763
  j =  2                              :            46111
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.40
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17911.33
p-value of test                       :  5.3e-3



-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.01
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.68
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.15
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.70
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.11
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.02
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9698.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.56
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000066367

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.73
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000061081

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51871775.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:47.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.93
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:29.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.49
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:00.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907871
  j =  2                              :            46057
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907781
  j =  2                              :            46102
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.39
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.21
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.71
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.04
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.26
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.90
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.06
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5202.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.03
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.79
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.59
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.07
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.05
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000194596

Normal statistic for number of bits   :    1.54
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.85
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000060319

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:58.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52953119.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.16
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:29.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.53
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908495
  j =  2                              :            45751
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908350
  j =  2                              :            45819
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.79
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17745.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.73
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.92
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.82
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.65
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.21
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.80
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.08
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.12
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.27
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.44
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000144100

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.29
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000026755

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         : 9.78e-3
p-value of test                       :    0.50

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:32.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54001695.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:45.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6932.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.20
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.95
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908396
  j =  2                              :            45799
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45509
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869509
  j =  1                              :        399908985
  j =  2                              :            45503
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.98
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.80
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.93
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   22.29
p-value of test                       :  1.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.59
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.96
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.08
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.91
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.64
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.90
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.03
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:32.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5182.01
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.59
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999919382

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.57
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000280351

Normal statistic for number of bits   :    2.22
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:40.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 70  MatrixRank, L=5000              1.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55050271.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5536
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:45.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.95
p-value of test                       :  3.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:47.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.42
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908258
  j =  2                              :            45865
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45597
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869597
  j =  1                              :        399908807
  j =  2                              :            45595
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.85
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.39
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   70.53
p-value of test                       :  5.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   51.78
p-value of test                       :  8.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.79
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.49
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.34
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.08
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.55
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.19e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.23
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.39
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999969236

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.00
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000081589

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:00.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 H (L=50, r=25)      5.1e-4
 75  RandomWalk1 R (L=50, r=25)      8.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56066079.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:45.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.89
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9928


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:49.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.99
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.81
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.44
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.69
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46226
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870226
  j =  1                              :        399907551
  j =  2                              :            46220
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46239
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870239
  j =  1                              :        399907525
  j =  2                              :            46233
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-4
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.69
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.09
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.49
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.94
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.61
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.28
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.65
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.78
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.22
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.78
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.35
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.93
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.30
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:36.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5095.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.17
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999972359

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.11
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000089935

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    2.46
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:51.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 J (L=50, r=0)       0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57114655.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    3.36
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:48.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   25.68
p-value of test                       :  5.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7223.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:28.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.29
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908163
  j =  2                              :            45908
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908282
  j =  2                              :            45853
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.94
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.23
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.31
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.66
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.05
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.61
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.56
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.00
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.81
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5097.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.34
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999991493

Normal statistic for number of bits   :  -0.067
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.06
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999908384

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:22.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                5.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58163231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.35
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.34
p-value of test                       :  6.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.85
p-value of test                       :  3.6e-3

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    3.97
p-value of test                       :  9.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     119
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:51.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  287.62
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7394.05
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.51
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:29.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.31
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908286
  j =  2                              :            45854
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908043
  j =  2                              :            45974
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:12.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.29
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17651.25
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.35
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.51
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.74
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.30
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.87
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.45
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.30
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.15
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.71
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4313.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.21
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000012682

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.97
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999970031

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:07.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59179039.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:33.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.49
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     537
p-value of test                       :    0.9952

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:28.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.61
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907914
  j =  2                              :            46040
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908095
  j =  2                              :            45948
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.28e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17653.03
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.79
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.05
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.25
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.09
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.25
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.23
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.05
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:41.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.05
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999991526

Normal statistic for number of bits   :  -0.067
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999901772

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  7.0e-3

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         : 5.88e-3
p-value of test                       :    0.50

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:22.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60162079.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.81
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:47.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:29.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.61
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.32
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908546
  j =  2                              :            45718
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907584
  j =  2                              :            46205
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    5.15
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  1.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.95
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.09
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.39
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.74
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.41
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.15
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.09
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.68
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.96
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.04
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4331.82
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12093.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.63
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999913028

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.66
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000011662

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:30.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61210655.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:19.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    3.22
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.97e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.75
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908401
  j =  2                              :            45792
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45602
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869602
  j =  1                              :        399908801
  j =  2                              :            45592
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:11.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.63e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -9.92e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.50
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.86
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.57
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.27
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.61
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.20
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.03
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.79
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.50
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.29
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.31
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.17
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.86
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.59
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.99
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999828800

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.96
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000098575

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:24.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62259231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5546
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:36.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.30
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.50
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:28.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.72
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.48
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908293
  j =  2                              :            45852
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45520
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869520
  j =  1                              :        399908964
  j =  2                              :            45512
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17073.68
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.72
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.93
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.60
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.50
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.44
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.19
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.65
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.90
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:21.63

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12103.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.25
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000032605

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.04
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999960473

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n95, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:50.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63275039.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:35.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   23.89
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.50
p-value of test                       :    0.9921


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4794.75
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:54.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45642
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869642
  j =  1                              :        399908719
  j =  2                              :            45636
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908619
  j =  2                              :            45686
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.69e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:27.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.040
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.10
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.22
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.53
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.56
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.30
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.04
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.70
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.16
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.88
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.89
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.45
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999916823

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.09
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000050821

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:11.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42565632.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6769.77
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:29.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.85
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.97
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:59.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908459
  j =  2                              :            45763
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908253
  j =  2                              :            45863
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-6
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.83
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.94
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.29
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.25
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.68
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.26
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.81
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.15
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  297.45
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.87
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.99
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.46
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.21
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.95e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.72
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999953183

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.96
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000076318

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :  -0.019
p-value of test                       :    0.51

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:08.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44367872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     968
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:28.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908392
  j =  2                              :            45798
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908443
  j =  2                              :            45771
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.7e-3


-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.51
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.87
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.99
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  584.73
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.73
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.39
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.33
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.65
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.85
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.72
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.37
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9727.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11618.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.46
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999959861

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.74
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000027334

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:49.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45285376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5294
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    4.65
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.71
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4802.70
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908455
  j =  2                              :            45768
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908349
  j =  2                              :            45824
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945


-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.37
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.67e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  105.86
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.14
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.28
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17753.84
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.97
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  579.83
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.34
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.16
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.33
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.22
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.32
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.28
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.18
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.15
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999976745

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.15
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000077902

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:34.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46432256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.28
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.97
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908147
  j =  2                              :            45919
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908585
  j =  2                              :            45703
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.96e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.62
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17182.54
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.86
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.82
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.15
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.47
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.17
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.10
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.81
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.10
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  480.44
p-value of test                       :  2.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.23
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.00
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.23
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  264.30
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.05
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000007270

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.20
p-value of test                       :  5.3e-3


-----------------------------------------------
Total number of bits:  7999845267

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:55.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   2.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47218688.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.09
p-value of test                       :  8.0e-3

Test on the Nm values of W_{n,i}(mNP1):    5.62
p-value of test                       :  1.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.05
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    3.38
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     185
p-value of test                       :  3.2e-3

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6903.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.04
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.14
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46378
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870378
  j =  1                              :        399907246
  j =  2                              :            46374
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908762
  j =  2                              :            45616
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:53.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.03e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   57.73
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.15
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.26
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.92
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.26
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.97
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.68
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.04
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.88
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.41
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.34
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.58
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.15
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.38
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.63
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.73
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9691.11
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.71
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4295.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11539.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.40
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999963812

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.72
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999886565

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:57.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48496640.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.02
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.19
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908080
  j =  2                              :            45957
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908341
  j =  2                              :            45822
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.9937

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:29.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17325.23
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.34
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.26
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.95
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.32
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.51
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.45
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.30
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.21
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.78
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:39.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.78
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999902075

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.16
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000106861

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:00.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49479680.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7076
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    3.49
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.49
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.44
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908294
  j =  2                              :            45850
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908331
  j =  2                              :            45824
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.61
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.23
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.73
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.35
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.47
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.95
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.67
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.69
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.42
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.18
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.67
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3914.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12136.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.40
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999865178

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.75
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999988889

Normal statistic for number of bits   :  -0.088
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:13.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50593792.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5235
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9946


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    4.06
p-value of test                       :  8.2e-3

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.17
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4828.15
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908582
  j =  2                              :            45703
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908076
  j =  2                              :            45959
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:15.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:15.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.86
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.76
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.24
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.92
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.40
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.83
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.52
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.06
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4331.52
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11531.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.79
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000114982

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.93
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000024256

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.36e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:04.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51544064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9978

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    3.40
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.28
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.14
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.9906

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.02
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:29.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.29
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.64
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908158
  j =  2                              :            45918
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46304
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870304
  j =  1                              :        399907396
  j =  2                              :            46296
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.51
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.48
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.32
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.36
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.90
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.76
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.47
p-value of test                       :  9.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.99
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.91
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.03
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.18
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999974033

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.55
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999877232

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52494336.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.64
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4907.09
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908842
  j =  2                              :            45570
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907880
  j =  2                              :            46054
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 5.34e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16940.90
p-value of test                       :    0.9959



-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.78
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.93
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.15
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.78
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.06
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.01
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.27
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.51
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.86
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000069463

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.09
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000025063

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:53.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53542912.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9903

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7298.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.74
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.66
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908282
  j =  2                              :            45856
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907751
  j =  2                              :            46120
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.21
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.86
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17727.93
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.03
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.88
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.37
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.98
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.93
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.74
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.71
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999939437

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.76
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999881885

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.091
p-value of test                       :    0.54

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:53.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54525952.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    3.91
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.88
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.12
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:02:38.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5173.89
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908005
  j =  2                              :            45990
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908313
  j =  2                              :            45842
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.17e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.27
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.90
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.86
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.47
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.70
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.83
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.51
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.14
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.99
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.37
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.93
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.23
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.38
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.76
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4318.07
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.21
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000037726

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.43
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000023692

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:27.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55541760.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908357
  j =  2                              :            45817
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908132
  j =  2                              :            45931
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  2.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.75e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17850.15
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.29
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.47
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.48
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.08
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.98
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.35
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.12
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.24
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.69
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.74
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.98
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10293.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.40
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999969392

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.98
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999951254

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.8e-3

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:36.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56590336.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:29.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7565
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.33
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.39
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.56
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.64
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.57
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4902.11
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908576
  j =  2                              :            45709
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45449
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869449
  j =  1                              :        399909106
  j =  2                              :            45441
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.02
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.46
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.99
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  465.88
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.37
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.88
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.47
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.51
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.01
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.34e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.91
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.58
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.32
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000112387

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.81
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000054532

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    2.56
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:13.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57704448.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997139
  j =  2                              :             1429
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    3.36
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     349
p-value of test                       :  3.1e-3

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1250.44
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6903.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   35.44
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.04
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.52
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908260
  j =  2                              :            45864
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908311
  j =  2                              :            45837
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.56e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   38.65
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.77
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.32
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.79
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.37
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.11
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.51
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.56
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.14
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.29
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.04
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.29
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.79
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -403.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.65
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 1.23e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3907.09
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.77
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999875714

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.52
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999938777

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  4.3e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    7.23
p-value of test                       :  2.8e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -2.88
p-value of test                       :    0.9980

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:51.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                      0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59179008.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.21
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.66
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.50
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.39
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.68
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.25
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:56.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46201
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870201
  j =  1                              :        399907602
  j =  2                              :            46193
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908358
  j =  2                              :            45815
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.58
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.75
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.45
p-value of test                       :    0.9961


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.07
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.19
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.63
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.66
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.86
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.41
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.79
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.53
p-value of test                       :  9.0e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.18
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.72
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.43
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.50
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999929828

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.91
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999840830

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:41.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60227584.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.66
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.96
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907935
  j =  2                              :            46022
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908323
  j =  2                              :            45834
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.67e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.72
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.96
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.88
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.87
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.94
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.03
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.30
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.00
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5175.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.79
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.38e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.64
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12142.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.57
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999885254

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.69
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999721526

Normal statistic for number of bits   :   -2.20
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         : 1.08e-3
p-value of test                       :    0.50

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:03.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61374464.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    3.00
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.74
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.08
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:30.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.51
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.57
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:59.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907737
  j =  2                              :            46121
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908040
  j =  2                              :            45977
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.71
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.84
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.89
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.58
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.36
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.30
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.43
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.61
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.61
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.24
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-3
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5169.82
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.48
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000046321

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.71
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000033121

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    2.58
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:29.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62259200.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.85
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.97
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.79
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45772
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869772
  j =  1                              :        399908461
  j =  2                              :            45762
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908486
  j =  2                              :            45754
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.59
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.02
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   73.88
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.46
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.78
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.05
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.32
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.30
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.62
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.53
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 9.36e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.07
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999880961

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.58
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000159625

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:54.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 H (L=50, r=25)      2.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63176704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    4.60
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9986

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.94
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  9.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   55.25
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.62
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907908
  j =  2                              :            46040
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908297
  j =  2                              :            45850
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.79
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.08
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.97
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.85
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  309.83
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.12
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.19
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  464.18
p-value of test                       :  1.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.32
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.93
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.33
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.62
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000025747

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.73
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000165088

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:28.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42598401.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4175
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:29.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.49
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45505
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869505
  j =  1                              :        399908994
  j =  2                              :            45497
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907659
  j =  2                              :            46169
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.41e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.92
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:27.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17120.35
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.63
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.15
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.61
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.09
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.57
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.80
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.61
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.33
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.98
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.86e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.15
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.06
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.17
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.46
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999887603

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.56
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999953612

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.052
p-value of test                       :    0.48

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:56.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43974657.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.29
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.86
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.89
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.42
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.26
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46246
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870246
  j =  1                              :        399907512
  j =  2                              :            46238
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908194
  j =  2                              :            45897
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.63
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.78
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.21
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.31
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.84
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  311.70
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.14
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.33
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.78
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :  1.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  151.61
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.014
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.18
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000125857

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.34
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999979364

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:49.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 28  SimpPoker, r = 0                0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44662785.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.06
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908206
  j =  2                              :            45891
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46172
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870172
  j =  1                              :        399907659
  j =  2                              :            46166
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.73e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.51e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.47
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.22
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.15
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.12
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.38
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.28
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.04
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.34
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    2.58
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.85
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.59
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.28
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.73
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000039427

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.19
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000101662

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:59.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            7.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45744129.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  340.25
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.29
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.88
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45425
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869425
  j =  1                              :        399909154
  j =  2                              :            45417
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45517
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869517
  j =  1                              :        399908971
  j =  2                              :            45507
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  7.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-5
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.82
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17536.17
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.60
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.90
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.37
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.10
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.51
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4828.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.00
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.27
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.48
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.61
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.22
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.84
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000057793

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.89
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999938216

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.023
p-value of test                       :    0.51

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:04.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 35  Gap, r = 25                     0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47087627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.69
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  356.48
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6881.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.85
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5174.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:49.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907586
  j =  2                              :            46201
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907810
  j =  2                              :            46089
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.37
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.21
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  191.60
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.97
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.98
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.21
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.24
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  299.52
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.85
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.10
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.15
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12218.63
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12179.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.59
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000039235

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.87
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000006550

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:48.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9995 
 79  RandomWalk1 H (L=10000, r=15)   0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48267275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4478
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.30
p-value of test                       :  7.4e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9940

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  291.00
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.89
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.45
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:50.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908190
  j =  2                              :            45902
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908151
  j =  2                              :            45917
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.04
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.83
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.44
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.34
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.17
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.91
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.20
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  1.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.28
p-value of test                       :  2.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.73
p-value of test                       :    0.9968

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.51
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.32
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.89
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999768341

Normal statistic for number of bits   :   -1.83
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.70
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999990416

Normal statistic for number of bits   :  -0.076
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:24.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP, t = 5           7.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49184779.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:16.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.55
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.33
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:33.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.05
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.58
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907877
  j =  2                              :            46051
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908048
  j =  2                              :            45970
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.36
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.31
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.95
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.94
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.83
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.09
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.69
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.75
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  462.77
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10238.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:33.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9997    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.95
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000057196

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.51
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000089785

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:49.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50069515.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:16.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.36
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.07
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908009
  j =  2                              :            45991
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45507
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869507
  j =  1                              :        399908994
  j =  2                              :            45491
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.33
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.70
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.59
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.97
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.84
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.79
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.57
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.58
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.10
p-value of test                       :    0.9948


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.44
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9639.98
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11274.77
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.18
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000041653

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.49
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999990323

Normal statistic for number of bits   :  -0.077
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:39.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 99  HammingIndep, L=1200, r=0       0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51118091.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    4.26
p-value of test                       :  6.5e-3

Stat. AD after spacings (mNP2-S)      :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.20
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.34
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46277
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870277
  j =  1                              :        399907449
  j =  2                              :            46271
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908562
  j =  2                              :            45710
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.85e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.37e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.89
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.52
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.72
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.16
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.31
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.48
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.14
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.89
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999984014

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.61
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000092458

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.044
p-value of test                       :    0.52

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:33.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52166667.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:32.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.34
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.14
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:59.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908481
  j =  2                              :            45758
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46173
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870173
  j =  1                              :        399907657
  j =  2                              :            46167
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.66
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.60
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.52
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.57
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.54
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5230.46
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.85
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.03
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.16
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.32
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000204547

Normal statistic for number of bits   :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.09
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999977825

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:12.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53215243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  284.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.93
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.50
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908250
  j =  2                              :            45872
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907909
  j =  2                              :            46044
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.42
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  411.69
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.90
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.20
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.24
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.10
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9733.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.33
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000042262

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.07
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000071323

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:07.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54263819.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    7.07
p-value of test                       :  3.2e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     666
p-value of test                       :  4.2e-3

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    4.99
p-value of test                       :  2.9e-3

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.95
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.00
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.54
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908485
  j =  2                              :            45756
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908005
  j =  2                              :            45993
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.65e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.80
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.18
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.47
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.10
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.05
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.10
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.25
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.34
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.83
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.21
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    5.05
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5193.51
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000133813

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.27
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999827660

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:43.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          3.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55345163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  373.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.31
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.65
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.51
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908169
  j =  2                              :            45914
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908298
  j =  2                              :            45845
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17544.26
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.10
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  586.47
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.69
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.81
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.52
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.79
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.56
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.57e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10267.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9755.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:32.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4318.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.07
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000174205

Normal statistic for number of bits   :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.61
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000108019

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:24.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56393739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5306
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    5.02
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.67
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908011
  j =  2                              :            45984
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908403
  j =  2                              :            45794
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    7.10
p-value of test                       :  3.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   36.80
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.35
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17495.66
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.54
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.98
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.29
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.22
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.71
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.95
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.81
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.57
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.63
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.22
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.51
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.01
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.24
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.80
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.85
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10233.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.23
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000135004

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.13
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000050338

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.037
p-value of test                       :    0.51

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft, t = 8                   0.9997 
 59  WeightDistrib, r = 0            0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57442315.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997243
  j =  2                              :             1377
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    3.72
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1540.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6864.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.35
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.64
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908074
  j =  2                              :            45957
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46332
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870332
  j =  1                              :        399907340
  j =  2                              :            46324
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-5
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17170.86
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.34
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.59
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.91
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.63
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.40
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.30
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.25
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.27
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.27
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.14e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4312.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.90
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000008821

Normal statistic for number of bits   :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000085507

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:50.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58490891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:36.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:46.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.53
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907880
  j =  2                              :            46057
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907736
  j =  2                              :            46132
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.60
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   55.34
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17112.21
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.32
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.57
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  425.75
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.81
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.93
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.52
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.54
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.32
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.34e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:29.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.33
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000035809

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.24
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999988532

Normal statistic for number of bits   :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:08.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59539467.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9943


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    3.29
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.22
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.85
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908275
  j =  2                              :            45855
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45393
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869393
  j =  1                              :        399909214
  j =  2                              :            45393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.92
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.20
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.51
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.81
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.62
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.07
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.69
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.66
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.80
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.75
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.23
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.96
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.58
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999983696

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.56
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999859976

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:25.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60588043.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:20.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.83
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:25.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907849
  j =  2                              :            46071
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908018
  j =  2                              :            45985
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17719.82
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.27
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.04
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.09
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.02
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.98
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999885410

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.90
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999844577

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:21.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61636619.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.86
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.18
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.42
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907856
  j =  2                              :            46066
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908582
  j =  2                              :            45709
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:19.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:12.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.52
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.01
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.76
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.01
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.09
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.08
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.75
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.02
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.87
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.23
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9707.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.73
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999958517

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.56
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000043795

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:44.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62717963.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.58
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.26
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.38
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:56.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908350
  j =  2                              :            45819
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908263
  j =  2                              :            45867
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -8.49e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17531.94
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.31
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.72
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.82
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.51
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.50
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.24
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -403.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.67
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.97
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -2.03e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.99
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.59
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000111874

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.93
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999876227

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:47.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42631170.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.45
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    : 3.16e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.09
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.84
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.43
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.69
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908431
  j =  2                              :            45777
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907908
  j =  2                              :            46037
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.52e-5
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.69
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.61
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.11
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.71
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.47
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.04
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.28
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9755.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.17
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999970361

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.30
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999975548

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:17.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43614210.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    3.82
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.08
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6904.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:33.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.54
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908681
  j =  2                              :            45658
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908161
  j =  2                              :            45915
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.69
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.83
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.89
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.48
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.81
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.51
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.07
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.14
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4687.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.32
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.40
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000120037

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.58
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000036136

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:22.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44728322.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997273
  j =  2                              :             1362
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9980

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1559.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:53.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.23
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.88
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908276
  j =  2                              :            45859
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908912
  j =  2                              :            45541
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.65e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.63
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.70
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.66
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.36
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.43
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.13
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.38
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.96
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  294.80
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.28
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.72
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.47e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.55
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.60
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000027577

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.57
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999842978

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         : -5.16e-3
p-value of test                       :    0.50

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:36.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45776898.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.12
p-value of test                       :  2.7e-3

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    3.61
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:30.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  172.40
p-value of test                       :  1.0e-3


-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907787
  j =  2                              :            46105
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907710
  j =  2                              :            46136
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -9.58e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.47
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17329.02
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.45
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.83
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   91.09
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.37
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.55
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.60
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.82
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.67
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.78
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.59
p-value of test                       :    0.9911

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.97
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.33
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.04
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999963776

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999820295

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:47.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46989314.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4184
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.92
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7292.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:33.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.27
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.69
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46298
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870298
  j =  1                              :        399907408
  j =  2                              :            46290
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908510
  j =  2                              :            45739
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.22
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.22
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  119.76
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.44
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  463.67
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.34
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.65
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.76
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.89
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.14
p-value of test                       :  5.3e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.95e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.60
p-value of test                       :  3.9e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.17
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.69
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.91
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999971360

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   27.60
p-value of test                       :    0.9989


-----------------------------------------------
Total number of bits:  8000067756

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:17.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)    6.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48037890.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1320.52
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.47
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.33
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46169
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870169
  j =  1                              :        399907666
  j =  2                              :            46161
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908208
  j =  2                              :            45890
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   74.83
p-value of test                       :  6.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17258.54
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.57
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.18
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.98
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.32
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.47
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.22
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.63
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.10
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.87
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.80
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.44
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999920264

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.39
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999926273

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:02.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           6.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49053698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    8.45
p-value of test                       :  8.3e-5    *****

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.83
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:35.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.73
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:57.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908356
  j =  2                              :            45819
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908709
  j =  2                              :            45641
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.30e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.54
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.48
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.50
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.56
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.84
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.46
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.36
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.77
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5078.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.35
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999993587

Normal statistic for number of bits   :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.13
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999947426

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.18
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:49.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP, t = 16          8.3e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50036738.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     179
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.44
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908265
  j =  2                              :            45860
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908041
  j =  2                              :            45972
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:27.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.37
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.26
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.33
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.44
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.83
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.73
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.04
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.63
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.42
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.72
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.01
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.37
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.62
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.76
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999935144

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.59
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999908270

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.98e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.72
p-value of test                       :    0.9967

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.50
p-value of test                       :    0.9938

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51085314.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:34.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.54
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.18
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4890.22
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45556
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869556
  j =  1                              :        399908890
  j =  2                              :            45552
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46296
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870296
  j =  1                              :        399907409
  j =  2                              :            46294
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.10e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.44
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.04
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.63
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  109.40
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.56
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.69
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.93
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.13
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.53
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.92
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.57
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.19
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.65
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    3.17
p-value of test                       :  7.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.45
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999859232

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.58
p-value of test                       :  7.4e-3


-----------------------------------------------
Total number of bits:  8000030730

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:09.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 92  HammingCorr, L = 30             0.9999 
 93  HammingCorr, L = 300            7.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52133890.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1490
p-value of test                       :  4.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334610
  j =  1                              :        599997020
  j =  2                              :             1490
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908409
  j =  2                              :            45791
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45471
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869471
  j =  1                              :        399909061
  j =  2                              :            45465
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:19.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17269.20
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.12
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.91
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.43
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.83
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.20
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.57
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.33
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.23
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -401.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.33
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9747.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.07
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999999947

Normal statistic for number of bits   : -4.19e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.95
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999967619

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:08.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           4.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53149706.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:38.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7083
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   25.46
p-value of test                       :  6.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6827.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.23
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.14
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:27.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908231
  j =  2                              :            45877
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908262
  j =  2                              :            45863
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-4
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    : 2.25e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17103.89
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.61
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.05
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.05
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.88
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.97
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.00
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.64
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.66
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.59
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.80
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.93
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10461.15
p-value of test                       :  6.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.28
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000058165

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.51
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000019906

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:29.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                6.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 90  HammingWeight2, r = 0           6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54198282.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5306
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     969
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    3.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    4.14
p-value of test                       :  7.5e-3

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.86
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.63
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.81
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908224
  j =  2                              :            45882
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908003
  j =  2                              :            45997
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:12.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.73
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   47.97
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.81
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.77
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.56
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.77
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.43
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.74
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.47
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.46
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12100.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.19
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000088507

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999961082

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:57.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55279626.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  498.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.95
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.08
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907906
  j =  2                              :            46044
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908310
  j =  2                              :            45839
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:18.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17284.21
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.00
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.74
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.17
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.00
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.53
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.65
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.36
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:03:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.84
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.15
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.08
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999999137

Normal statistic for number of bits   : -6.82e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.45
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999968354

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:09.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56328202.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.81
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.08
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907955
  j =  2                              :            46021
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908365
  j =  2                              :            45813
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.95e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:12.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.92
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.83
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.68
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.74
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.06
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.50
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.47
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.88
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.52
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.88
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.76
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.02
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10335.21
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.19
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.69
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000068269

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.42
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999944264

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:22.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57376778.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9933

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7313.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.73
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.20
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.98
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908107
  j =  2                              :            45939
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908165
  j =  2                              :            45907
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:29.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:29.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17623.98
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.39
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.77
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.44
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.77
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.81
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.62
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.88
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.36
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.70e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.65
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.48
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:29.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.94
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999918863

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.78
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000007039

Normal statistic for number of bits   :   0.056
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         : -6.18e-3
p-value of test                       :    0.50

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:54.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58392586.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:20.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.80
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46197
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870197
  j =  1                              :        399907608
  j =  2                              :            46193
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:19.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:19.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.28
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.48
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.67
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.52
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.77
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.25
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.90
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.44
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.33
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.47
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.16
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.41
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.41
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.54
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.29
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.49
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.29
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.15
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000117256

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.91
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999935177

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:54.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59441162.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    4.64
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.02
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.19
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908413
  j =  2                              :            45789
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908114
  j =  2                              :            45937
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:29.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.15
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:28.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.96
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.81
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.52
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  199.83
p-value of test                       :  2.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.18
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.78
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.51
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.82
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.69
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.61
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.04
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999903893

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.20
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000002659

Normal statistic for number of bits   :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.74
p-value of test                       :  3.1e-3

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:04.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60456970.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:35.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.29
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.09
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45556
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869556
  j =  1                              :        399908891
  j =  2                              :            45550
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907772
  j =  2                              :            46108
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.28e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.66
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.13
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.12
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.35
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.54
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4778.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.79
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  253.19
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.25
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.11
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.04
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10253.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:49.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5084.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12272.17
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.91
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000035290

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.28
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999823364

Normal statistic for number of bits   :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:59.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61505546.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5553
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  372.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.91
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5287.66
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908531
  j =  2                              :            45727
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908162
  j =  2                              :            45910
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    4.30
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.53
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.21
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.09
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.44
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.99
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.88
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.24
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.25
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.61
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.86
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.95
p-value of test                       :    0.9985

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.24
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.99
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000192889

Normal statistic for number of bits   :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.48
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999886064

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:36.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62554122.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5247
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    3.66
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.02
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:59.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908379
  j =  2                              :            45803
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908282
  j =  2                              :            45853
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.19e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.41
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.00
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.93
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.29
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.14
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.93
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.33
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.47
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.79
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.49
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.73
p-value of test                       :    0.9969

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.31
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.64
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5070.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.23
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999922886

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.76
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999878387

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:39.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42663939.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997153
  j =  2                              :             1422
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.42
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.56
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.23
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907847
  j =  2                              :            46072
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908824
  j =  2                              :            45588
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17231.62
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.25
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.84
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.97
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.13
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.83
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.63
p-value of test                       :  4.3e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.18
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000109702

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.27
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999933992

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         : 1.00e-2
p-value of test                       :    0.50

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:02.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44105731.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.25
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.11
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.07
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.61
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908415
  j =  2                              :            45788
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908069
  j =  2                              :            45961
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    : 2.77e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    5.65
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:27.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.29
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17280.47
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.99
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.33
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.82
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.57
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.98
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4809.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.38
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.15
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.50
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5037.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3917.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11357.63
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.47
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000005578

Normal statistic for number of bits   :   0.044
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.96
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999886850

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : 6.12e-3
p-value of test                       :    0.50

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    2.67
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:21.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44892163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7528
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    5.61
p-value of test                       :  1.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     506
p-value of test                       : 1 -  4.5e-5    *****

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.50
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5257.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908608
  j =  2                              :            45684
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908788
  j =  2                              :            45597
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.70
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.28
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.57
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.03
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.09
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.86
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.93
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.90
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9737.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.47
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.20
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.56
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000090262

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.84
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000175870

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.6e-3

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.091
p-value of test                       :    0.54

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:01.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs NJumps, t = 5       1 -  4.5e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46071831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1557.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:29.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.38
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907941
  j =  2                              :            46019
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908708
  j =  2                              :            45643
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.29e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.76
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.78
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.71
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   55.73
p-value of test                       :  3.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.47
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.59
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.96
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.51
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.94
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.58
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.44
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.44
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5175.36
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.98
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999953516

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.31
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999895844

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:22.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 J (L=50, r=25)      3.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47349783.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.29
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.49
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:28.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.58
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.58
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.68
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908469
  j =  2                              :            45758
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46320
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870320
  j =  1                              :        399907367
  j =  2                              :            46306
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.78e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17068.19
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.19
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.93
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.00
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.05
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.73
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5330.78
p-value of test                       :  5.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.96
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.43
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -403.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.53e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.74
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.29
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.59
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000001483

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.79
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999943295

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : -7.48e-3
p-value of test                       :    0.50

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:14.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 J (L=10000, r=0)    5.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48463895.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1239
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334359
  j =  1                              :        599997522
  j =  2                              :             1239
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7338.88
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.73
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.86
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908701
  j =  2                              :            45642
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908229
  j =  2                              :            45881
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.50
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.72
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.44
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.90
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.88
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.07
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.80
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.89
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.04
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  266.23
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999985175

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.73
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000051133

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:23.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49545239.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.42
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.31
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.86
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907884
  j =  2                              :            46055
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46132
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870132
  j =  1                              :        399907739
  j =  2                              :            46126
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:02:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.88e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.47
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17643.72
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.02
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.22
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.11
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.04
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.13
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.33
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.05
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.16
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.76
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.65
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9737.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3868.92
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.17
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000075448

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.51
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999939140

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:42.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50462743.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.79
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.30
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.63
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.79
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46210
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870210
  j =  1                              :        399907584
  j =  2                              :            46202
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907755
  j =  2                              :            46115
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  4.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 2.83e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    6.48
p-value of test                       :  6.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.54e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -6.15e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.47
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.92
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.15
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.56
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.18
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.42
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.94
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.33
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10300.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.20
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000106603

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.73
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999996695

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:06.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              6.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51576855.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.10
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.58
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.21
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.69
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908255
  j =  2                              :            45868
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908241
  j =  2                              :            45869
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:52.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 2.81e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:27.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.72
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.94
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.35
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.60
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.65
p-value of test                       :    0.9959

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11578.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.47
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999906674

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.90
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999959636

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.046
p-value of test                       :    0.52

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:08.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52690967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.65
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.22
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4906.72
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908093
  j =  2                              :            45949
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46188
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870188
  j =  1                              :        399907627
  j =  2                              :            46182
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.84e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17706.39
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.49
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.48
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  446.96
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.08
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.45
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.50
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.08
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.87
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.33
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000142165

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.13
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999907805

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:19.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53641239.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    4.49
p-value of test                       :  5.1e-3

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6843.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.50
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908614
  j =  2                              :            45684
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45502
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869502
  j =  1                              :        399908999
  j =  2                              :            45496
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9939


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.41
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.09
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.06
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.48
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.33
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.08
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.53
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.99
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.21
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.47
p-value of test                       :    0.9912


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :   0.099
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.29e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.95
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.62
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.25
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000051394

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.66
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000047884

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:28.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54657047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.84
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908743
  j =  2                              :            45624
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908004
  j =  2                              :            45995
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.77
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.72
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.49
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.55
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.13
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.78
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.04
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.35
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.79
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.01
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5198.16
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3914.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.76
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000088849

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.77
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000234265

Normal statistic for number of bits   :    1.85
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:07.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55640072.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7521
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  510.02
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1365.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.76
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.25
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908406
  j =  2                              :            45791
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46246
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870246
  j =  1                              :        399907513
  j =  2                              :            46236
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.85e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 9.92e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.65
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.45
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.03
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.34
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.58
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.49
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.04
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.31
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.45
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.75
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10215.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11562.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11531.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.50
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000003115

Normal statistic for number of bits   :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.88
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000104869

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:45.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56819734.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.66
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.91
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45495
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869495
  j =  1                              :        399909015
  j =  2                              :            45485
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908752
  j =  2                              :            45621
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17314.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.76
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.50
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.21
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.74
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.96
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.50
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.56
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.45
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.48
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.85
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.61
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.43
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.15
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11617.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.22
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000035803

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.65
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999936695

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.00e-3
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.44
p-value of test                       :    0.9927

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:07.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57868310.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     839
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.88
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1283.06
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6914.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.34
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.33
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.55
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:02:59.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45463
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869463
  j =  1                              :        399909077
  j =  2                              :            45457
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908569
  j =  2                              :            45708
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.99
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.87
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.34
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.52
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4827.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.70
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.00
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.79
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.90
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    2.50
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.87
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:32.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.77
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.92
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999857999

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.84
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000048763

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.039
p-value of test                       :    0.48

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         : 1.00e-4
p-value of test                       :    0.50

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:45.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58785814.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.29
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.81
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.96
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.27
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.36
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.04
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908255
  j =  2                              :            45865
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907936
  j =  2                              :            46020
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.82e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.68
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17601.77
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  109.83
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.25
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.27
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.48
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.53
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.34
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.69
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.24
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000020200

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.38
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999987806

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:34.55
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59998230.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    4.18
p-value of test                       :  7.1e-3

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   80.46
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907994
  j =  2                              :            45997
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907995
  j =  2                              :            45992
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.53
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.46
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.20
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.82
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.35
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.45
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.75
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.85
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.27
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.53
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -8.44e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4691.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.37
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.97
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000120073

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.16
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000007435

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:34.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61046806.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:30.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:59.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.87
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.59
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908231
  j =  2                              :            45880
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908092
  j =  2                              :            45948
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9921


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.44e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.04
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.80
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.20
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.28
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.52
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.23
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 2.27e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.09
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.93
p-value of test                       :  4.6e-3


-----------------------------------------------
Total number of bits:  7999694274

Normal statistic for number of bits   :   -2.42
p-value of test                       :    0.9922



-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.64
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999996689

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:34.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62095382.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1505
p-value of test                       :  9.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334625
  j =  1                              :        599996990
  j =  2                              :             1505
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    8.44
p-value of test                       :  7.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:02:49.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.88
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.85
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.61
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908391
  j =  2                              :            45803
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908520
  j =  2                              :            45737
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.54
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.62
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.79
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.55
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.21
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.78
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5277.58
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.21
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.08
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.22
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.06
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.49
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999989690

Normal statistic for number of bits   :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.53
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999849788

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:55.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.2e-5
 25  ClosePairs mNP2S, t = 16        7.5e-5
 75  RandomWalk1 R (L=50, r=25)      0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63471638.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.33
p-value of test                       :  6.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.30
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.89
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1551.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.60
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.93
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907990
  j =  2                              :            45996
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908422
  j =  2                              :            45783
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  3.9e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    6.91
p-value of test                       :  3.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9990


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.13e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17648.23
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.39
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.34
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.80
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.67
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.58
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.59
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.97
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.84
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.25
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000029956

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.33
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000043384

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.051
p-value of test                       :    0.52

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:25.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42696708.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    3.31
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.53
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908214
  j =  2                              :            45887
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908554
  j =  2                              :            45714
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17374.13
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.01
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.67
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.01
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.04
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.65
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.40
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.92
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.42
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4288.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.84
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000047869

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.54
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000141817

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.44
p-value of test                       :  7.3e-3

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.20
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:42.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44007428.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7583
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9914

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:37.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7304.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.16
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.77
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:47.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907706
  j =  2                              :            46138
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.49e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17636.21
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.94
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.75
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.98
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.90
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5230.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.60
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.42
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.86
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4396.86
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.59
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999888845

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.10
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000109714

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:00.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44761092.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.43
p-value of test                       :  1.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.20
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.45
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:48.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908333
  j =  2                              :            45832
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907792
  j =  2                              :            46101
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.87e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.94
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17100.07
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.65
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.59
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.01
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.39
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.24
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.22
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.31
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.97
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.94
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999931496

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.01
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000091897

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:20.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45875204.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7564
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:31.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.93
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5141.24
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908174
  j =  2                              :            45910
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45411
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869411
  j =  1                              :        399909180
  j =  2                              :            45407
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17584.77
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.31
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.81
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.46
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.31
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.74
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.64
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.14
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.29
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.53
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 2.10e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.42
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999959378

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.19
p-value of test                       :  3.5e-3


-----------------------------------------------
Total number of bits:  8000186718

Normal statistic for number of bits   :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:50.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47153156.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4190
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.55
p-value of test                       :  4.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.14
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:51.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45471
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869471
  j =  1                              :        399909061
  j =  2                              :            45465
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907790
  j =  2                              :            46096
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 3.93e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.47
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.90
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.99
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.07
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.28
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.33
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  484.26
p-value of test                       :  3.8e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.27
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.81
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.83e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.65
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.99
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.20
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.59
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11548.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.40
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000175492

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.13
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000144976

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.36e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:08.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   3.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47972356.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1240
p-value of test                       :    0.9997    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334360
  j =  1                              :        599997520
  j =  2                              :             1240
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:39.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:33.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.28
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.33
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45655
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869655
  j =  1                              :        399908693
  j =  2                              :            45649
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46152
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870152
  j =  1                              :        399907698
  j =  2                              :            46148
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.89e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.88
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.64
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.23
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.24
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.27
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.30
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.73
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.60
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12159.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.25
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999770975

Normal statistic for number of bits   :   -1.81
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.67
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000031729

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.045
p-value of test                       :    0.52

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:49.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49086468.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  177.77
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:33.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.99
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  167.27
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:47.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907720
  j =  2                              :            46137
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45551
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869551
  j =  1                              :        399908902
  j =  2                              :            45543
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.05
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.52
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.42
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.83
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.66
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.54
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.83
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.49
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.31
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.50
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.42e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9745.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.95
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000042100

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.90
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000203686

Normal statistic for number of bits   :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:08.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50167812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1247
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334367
  j =  1                              :        599997506
  j =  2                              :             1247
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7129
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.22
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.98
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45447
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869447
  j =  1                              :        399909107
  j =  2                              :            45445
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908005
  j =  2                              :            45987
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.86e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17144.03
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.26
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.95
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.13
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.65
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.12
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.30
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.29
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.66
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.46
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.94
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.64
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.51
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.65
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.78
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11567.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.12
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000083449

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.09
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999896159

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:24.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51281939.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.63
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.24
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.41
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:52.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907720
  j =  2                              :            46131
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46241
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870241
  j =  1                              :        399907521
  j =  2                              :            46235
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 3.22e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17430.59
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.32
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.11
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.37
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.68
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.75
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.22
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.93
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.04
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.18
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5074.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12087.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999913667

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.01
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000046435

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:26.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52264979.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.94
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.10
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.54
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.81
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908358
  j =  2                              :            45818
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45416
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869416
  j =  1                              :        399909171
  j =  2                              :            45410
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.42e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.46
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.93
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   51.49
p-value of test                       :  9.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.15
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.30
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.03
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.30
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.91
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.42
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.32e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9719.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.34
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.31
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999910076

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.69
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000008311

Normal statistic for number of bits   :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         : -6.36e-3
p-value of test                       :    0.50

Sample variance                       :    0.21
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:15.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       9.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53313555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.27
p-value of test                       :  2.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.75
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.14
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.90
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907812
  j =  2                              :            46088
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45569
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869569
  j =  1                              :        399908863
  j =  2                              :            45567
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.75e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.56
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.71
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.12
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.81
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.39
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.73
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12115.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.62
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999938204

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.68
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000025384

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    2.54
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:45.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54362131.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    4.26
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.68
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6855.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.46
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.37
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:02:53.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908254
  j =  2                              :            45867
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907992
  j =  2                              :            45998
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.27e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.76
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.04
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.9900

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17897.18
p-value of test                       :  6.5e-3



-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.27
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.67
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.16
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.59
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.55
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.26
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.28
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.44
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.28
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.22
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:33.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.40
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999889070

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.73
p-value of test                       :  5.9e-3


-----------------------------------------------
Total number of bits:  8000109957

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:30.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55377939.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   35.59
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.26
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.59
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908441
  j =  2                              :            45778
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908735
  j =  2                              :            45628
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.64
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.35
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.24
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.47
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.60
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.30
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.65
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.33
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.62
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.33
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999955655

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.53
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999954233

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.045
p-value of test                       :    0.52

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:11.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56492051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.89
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:49.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:54.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907788
  j =  2                              :            46106
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908260
  j =  2                              :            45867
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9911


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.94
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17052.38
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   52.27
p-value of test                       :  7.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.14
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.48
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.44
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.78
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.82
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.74
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.42
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -3.18
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.80
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999957860

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.99
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000069376

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:36.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       7.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 93  HammingCorr, L = 300            0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57540627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  509.90
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.08
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.50
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908282
  j =  2                              :            45853
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45612
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869612
  j =  1                              :        399908778
  j =  2                              :            45608
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.89
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.09
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.88
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.31
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.17
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.65
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.32
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.45
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5175.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.19
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.98
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.23
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.96
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10316.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11459.13
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.54
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999939506

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.07
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000086638

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:04.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58589203.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.36
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    3.50
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:45.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  508.28
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.32
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:00.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908173
  j =  2                              :            45906
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908711
  j =  2                              :            45643
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.091
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17941.33
p-value of test                       :  3.3e-3



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.48
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.88
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4708.73
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.23
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.21
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.01
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.04
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.58
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10377.64
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4666.68
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12117.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.47
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000039286

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.57
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000061654

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:17.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59637779.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  181.41
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.94
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.26
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.60
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908191
  j =  2                              :            45900
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908114
  j =  2                              :            45937
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17226.61
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.62
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.65
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  420.22
p-value of test                       :    0.9960


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.51
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.31
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.58
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.28
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.22
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.85
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.20
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.87
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -3.00
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12191.71
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.75
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000055054

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999916271

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.056
p-value of test                       :    0.48

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:45.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60686355.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.09
p-value of test                       :  8.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :   11.05
p-value of test                       :  4.7e-6    *****

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.37
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6861.44
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.16
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.41
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908167
  j =  2                              :            45912
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908594
  j =  2                              :            45691
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9902


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:19.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17226.46
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.76
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.16
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.57
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.56
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.25
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.47
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.87
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.54
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.58
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.15
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.19
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.15e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.58
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000058804

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.53
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000147952

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:09.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           4.7e-6
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61702163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.04
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.60
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908520
  j =  2                              :            45734
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908094
  j =  2                              :            45953
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:19.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17238.92
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.69
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.96
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.27
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.60
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.28
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.28
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.44
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.59
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.80
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.07
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.24
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.67
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.56
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    : 2.11e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    4.47
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4598.36
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5092.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11552.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.38
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000051880

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.98
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000000022

Normal statistic for number of bits   : 1.74e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:00.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62783507.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.56
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.55
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.30
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.64
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907861
  j =  2                              :            46068
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908206
  j =  2                              :            45891
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.97e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.31
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.97
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.22
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.70
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.92
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.22
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999937706

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.16
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999983378

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:01.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42729478.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9997    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9919

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.21
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.16
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.82
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.08
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.75
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908009
  j =  2                              :            45991
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45632
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869632
  j =  1                              :        399908739
  j =  2                              :            45626
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17661.74
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.85
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.70
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.79
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.28
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.88
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.73
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.77
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.18
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5076.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11476.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.15
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.53
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000020854

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.35
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999976931

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:07.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44302350.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:29.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:46.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.70
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.30
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.46
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908071
  j =  2                              :            45960
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908302
  j =  2                              :            45846
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  6.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.28
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17570.66
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.11
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.52
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.57
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.74
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.61
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.58
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.18
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.38
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.87
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.01
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10292.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.45
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999842408

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.91
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999912059

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
p-value of test                       : 1 -  7.9e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.71
p-value of test                       :  3.4e-3

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:58:12.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45219854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    3.92
p-value of test                       :  9.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.14
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907650
  j =  2                              :            46166
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45433
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869433
  j =  1                              :        399909137
  j =  2                              :            45427
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.63e-4
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    : 1.58e-5
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    4.83
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.92
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.18
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.87
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.45
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  446.16
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.45
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.64
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.00
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.86
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999855419

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.79
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000010417

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:52.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46727182.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4478
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.49
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:53.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.65
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.28
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.99
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:28.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.38
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.14
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908330
  j =  2                              :            45829
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46008
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870008
  j =  1                              :        399907987
  j =  2                              :            46002
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.36
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  111.67
p-value of test                       :  5.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17383.75
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.54
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.42
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.37
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.28
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.96
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.78
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.76
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  145.12
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.31
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000037612

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.64
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000060073

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.13
p-value of test                       :    0.98

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:43.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 60  WeightDistrib, r = 20           5.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47775758.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.76
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.78
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46292
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870292
  j =  1                              :        399907424
  j =  2                              :            46276
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907814
  j =  2                              :            46087
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.72e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  118.66
p-value of test                       :  1.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.5e-4    *****

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.45
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.99
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.40
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.13
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.58
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  143.19
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.99
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.76
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.69
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999908936

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.11
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000058813

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:05.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 60  WeightDistrib, r = 20           1.0e-4
 78  RandomWalk1 C (L=10000, r=0)    0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48824334.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.99
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:28.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.53
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.14
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907965
  j =  2                              :            46016
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45469
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869469
  j =  1                              :        399909069
  j =  2                              :            45455
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.74e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17119.07
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.31
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.61
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.52
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.89
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.09
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.32
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.73
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.32
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.29
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.08
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.73
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999907832

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.70
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999973121

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.070
p-value of test                       :    0.53

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:10.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49872910.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.41
p-value of test                       :  5.6e-3

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.12
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:02:46.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6838.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.20
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.49
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908773
  j =  2                              :            45606
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908353
  j =  2                              :            45813
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.98e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.71e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:28.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.82
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.74
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.02
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.61
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.47
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.44
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.78
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.50
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.15
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.06
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.25
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999967472

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.71
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000043348

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:22.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        0.9997 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50921486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.47
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.27
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1552.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7244.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.59
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908608
  j =  2                              :            45687
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908745
  j =  2                              :            45623
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17607.99
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.58
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.23
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.91
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.63
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.91
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.08
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.42
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.49
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.26
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000105421

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.06
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999921863

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:16.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51937294.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9952

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:47.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.08
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907863
  j =  2                              :            46061
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907702
  j =  2                              :            46143
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-5
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.02
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.74
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.87
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.04
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.44
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.88
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.40
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.02
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.68
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.43
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999836477

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.45
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000043708

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:01.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52985870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:48.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.05
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.24
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.14
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5257.60
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46241
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870241
  j =  1                              :        399907521
  j =  2                              :            46235
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908250
  j =  2                              :            45869
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    4.74
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.09
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.65
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.56
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  601.17
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.54
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.03
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.92
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.27
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.78
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.47
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 4.51e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:35.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.75
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000094465

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.05
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000086662

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:39.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54001678.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9973

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.51
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.07
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.96
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907779
  j =  2                              :            46106
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907873
  j =  2                              :            46059
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 3.03e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.76e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.42
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.57
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.29
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.07
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.49
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.25
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.46
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11567.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000080212

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.69
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999958061

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    2.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:50.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55017486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9975

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.13
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.68
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4867.12
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46162
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870162
  j =  1                              :        399907677
  j =  2                              :            46160
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907964
  j =  2                              :            46009
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.71e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17641.00
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   49.55
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.47
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.91
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.20
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.64
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.69
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.79
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.13
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.97
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999992735

Normal statistic for number of bits   :  -0.057
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.05
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000030268

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:11.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56033294.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.63
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.91
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:47.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.69
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:29.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.00
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908375
  j =  2                              :            45808
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907960
  j =  2                              :            46017
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.47e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.09
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.78
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.18
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.01
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.47
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.99
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.86
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.50
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.55
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.36
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.61
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.22
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.15
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.03
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4306.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.32
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999840308

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.34
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000011767

Normal statistic for number of bits   :   0.093
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:08.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57016334.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    4.32
p-value of test                       :  6.1e-3

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.70
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.11
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908345
  j =  2                              :            45817
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908124
  j =  2                              :            45938
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17194.94
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.71
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.27
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.25
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.46
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.51
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.20
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.85
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4791.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.75
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.54
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.10
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000144730

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.83
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999983318

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:36.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58032142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9950


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   40.20
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1547.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.35
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.37
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908515
  j =  2                              :            45735
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908231
  j =  2                              :            45883
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   70.78
p-value of test                       :  6.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.76
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.52
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.62
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.87
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.53
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.04
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.50
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.69
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.19
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.22
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.44
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:31.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11610.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.16
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999987521

Normal statistic for number of bits   :  -0.099
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.16
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999954104

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.12
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:17.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           6.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59047950.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    3.40
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.35
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.74
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.58
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908202
  j =  2                              :            45893
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908578
  j =  2                              :            45705
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.86e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.79
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17465.17
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.53
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.52
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.65
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.15
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.19
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.24
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.66
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.93
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.44
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.11
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.60
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000097801

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.87
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000060904

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:44.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60030990.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:29.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.27
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.73
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908489
  j =  2                              :            45751
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46382
p-value of test                       :  9.6e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870382
  j =  1                              :        399907242
  j =  2                              :            46370
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.79
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.93
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.28
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.77
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.35
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.95
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.93
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4851.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.08
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.14
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.29
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.28
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.80
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.41
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999950750

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.07
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000016696

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.034
p-value of test                       :    0.49

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:29.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61145102.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9982


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9914

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.76
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:30.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.96
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908092
  j =  2                              :            45945
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46146
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870146
  j =  1                              :        399907711
  j =  2                              :            46140
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -2.61e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.62
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.10
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.52
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.21
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.72
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.01
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.15
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.58
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.35
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.38
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999824009

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.66
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000077380

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:25.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62160910.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.22
p-value of test                       :  7.0e-3

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.09
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:59.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908192
  j =  2                              :            45898
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46138
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870138
  j =  1                              :        399907728
  j =  2                              :            46130
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.45
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.54
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.16
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.81
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.99
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.48
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.63
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -401.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.69
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999914747

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.87
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000122689

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    6.91
p-value of test                       :  4.0e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.56
p-value of test                       :    0.9998    *****

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:26.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 106  AutoCor, d=3, r=27              0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63209486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.88
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:28.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.25
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.04
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908252
  j =  2                              :            45868
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908383
  j =  2                              :            45804
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17605.33
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.78
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.12
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.06
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.15
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.71
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.65
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.49
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.89
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.86
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.14
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000099196

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999989480

Normal statistic for number of bits   :  -0.083
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:49.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42762247.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.94
p-value of test                       :  9.5e-3

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1557.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6772.31
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.68
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:58.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908168
  j =  2                              :            45907
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46193
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870193
  j =  1                              :        399907620
  j =  2                              :            46181
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.68e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.96
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.13
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   44.12
p-value of test                       :  3.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.20
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.85
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.15
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.18
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.80
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.91
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.66
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.47
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.04
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.10
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.44
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.07
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999967415

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.53
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999924230

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:35.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      3.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44171271.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    5.73
p-value of test                       :  1.3e-3

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.90
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.90
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5202.24
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908194
  j =  2                              :            45897
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907762
  j =  2                              :            46110
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.14e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.78
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   68.46
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.43
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.10
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.55
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.70
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.78
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.12
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12141.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.26
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000049348

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.32
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999968951

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:59.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       6.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45383687.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.58
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.63
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.97
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:52.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907726
  j =  2                              :            46128
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45626
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869626
  j =  1                              :        399908751
  j =  2                              :            45620
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:27.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17115.95
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  199.15
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.73
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.14
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.93
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.51
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.98
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.11
p-value of test                       :  9.9e-3


-----------------------------------------------
Total number of bits:  8000032140

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.55
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000011227

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Tests on the sum of all N observations
Standardized normal statistic         :   0.096
p-value of test                       :    0.46

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:36.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46268423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.47
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.60
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.26
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907974
  j =  2                              :            46007
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908628
  j =  2                              :            45683
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.23
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.051
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.48
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.42
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.79
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.79
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.86
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.32
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.39
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.84
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.49
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.37
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.63
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.30
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11433.15
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.06
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000107641

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999881978

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.023
p-value of test                       :    0.51

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:10.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47022087.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5282
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:36.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.57
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:31.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.28
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4903.07
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:51.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908176
  j =  2                              :            45903
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908551
  j =  2                              :            45717
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.87e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.98
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.34
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.65
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.15
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   39.64
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.99
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.50
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.65
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.59
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.25
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.34
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.63
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9790.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11483.89
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.55
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999959063

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.25
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999956762

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:43.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48234503.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.13
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:33.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.90
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.37
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908638
  j =  2                              :            45675
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908365
  j =  2                              :            45813
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17898.20
p-value of test                       :  6.4e-3



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.01
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.61
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.55
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.87
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.69
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  308.11
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.04
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.49
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.61
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.50
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.75
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.79
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.85
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000042304

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.48
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999980762

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:36.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49020935.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.41
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:33.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.50
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.44
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908349
  j =  2                              :            45824
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907887
  j =  2                              :            46049
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.96e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17983.08
p-value of test                       :  1.7e-3



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.96
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.28
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.51
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.67
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.40
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  8.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.69
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10212.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.37
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.77
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999891827

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000108748

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:09.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50102279.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5278
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:33.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.28
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.13
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907952
  j =  2                              :            46021
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907952
  j =  2                              :            46021
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.18e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.80
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.42
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.53
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.34
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.02
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.72
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.80
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.63
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.04
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    2.67
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.63
p-value of test                       :    0.9904

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:33.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5102.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.09
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000003082

Normal statistic for number of bits   :   0.024
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.46
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999930812

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:31.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51150855.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4508
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.06
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.78
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7234.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:31.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.42
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.72
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:57.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908109
  j =  2                              :            45932
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908696
  j =  2                              :            45649
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.21
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.19
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.07
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4805.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  298.30
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.73
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.63
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.68
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4761.76
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.15
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.83
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.13
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10291.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.72
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000015886

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.15
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000008032

Normal statistic for number of bits   :   0.063
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:57.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52232199.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7250.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.96
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.82
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907747
  j =  2                              :            46125
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45515
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869515
  j =  1                              :        399908974
  j =  2                              :            45507
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.22
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.08
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.02
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  301.08
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.92
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.01
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.48
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.9900

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9705.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5066.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4278.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.10
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999852131

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.30
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999937778

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:02.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53411847.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9950

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.04
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5226.20
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907780
  j =  2                              :            46107
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908349
  j =  2                              :            45821
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:14.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   32.30
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17146.49
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.07
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.50
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.77
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.86
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.31
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.06
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.28
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  305.17
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.40
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.69
p-value of test                       :  6.1e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.34
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  153.13
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:02:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10262.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.36
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.23
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999954134

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.25
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000143902

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:15.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 59  WeightDistrib, r = 0            0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54460423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4167
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.09
p-value of test                       :  2.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    4.01
p-value of test                       :  8.6e-3

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6814.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.66
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.04
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:56.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908490
  j =  2                              :            45746
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908626
  j =  2                              :            45684
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17607.93
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.71
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.64
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.93
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.97
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5175.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.16
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.88
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.15
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.84
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11588.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.45
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000048652

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999868151

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    4.68
p-value of test                       :  4.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.89
p-value of test                       :  1.9e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:07.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55410695.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4204
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.60
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.73
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908047
  j =  2                              :            45972
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908717
  j =  2                              :            45631
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.38e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17427.57
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.56
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.69
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.57
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.02
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.46
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.46
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.01
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4711.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.46
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.21
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999963917

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.65
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999909323

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:54.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56459271.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.95
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.63
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908614
  j =  2                              :            45693
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908424
  j =  2                              :            45782
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.87
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.70
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.45
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.00
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.80
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.21
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.22
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.43
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5069.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.52
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000047650

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.60
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999833468

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.21
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:51.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57507847.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5281
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.83
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.47
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:28.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.76
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.99
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908043
  j =  2                              :            45974
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908606
  j =  2                              :            45694
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.42
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17663.84
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.37
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.39
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.30
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.32
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.21
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.42
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.29
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.41
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.28
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.33
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.18
p-value of test                       :    0.9964


-----------------------------------------------
Total number of bits:  7999983384

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.97
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999889169

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:15.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58556423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7140.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.77
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.17
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.06
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908160
  j =  2                              :            45917
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908519
  j =  2                              :            45736
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17022.22
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.27
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.81
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.64
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.21
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.18
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.05
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12145.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.31
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999943220

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.92
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000012469

Normal statistic for number of bits   :   0.099
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:07.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59604999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.93
p-value of test                       :  9.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.20
p-value of test                       :  7.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.17
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:49.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.82
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908167
  j =  2                              :            45912
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907733
  j =  2                              :            46129
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.69e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   16.79
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.37
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.47
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.75
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.77
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.18
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.07
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.40
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.37
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.53e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.37
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4299.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3903.88
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11517.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.72
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999978086

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.32
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000016645

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:09.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60653575.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    3.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.39
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.95
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908390
  j =  2                              :            45796
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908040
  j =  2                              :            45971
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17446.80
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.26
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.27
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.70
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.79
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.94
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.48
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.05
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.72
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.58
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:29.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.99
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000032476

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.06
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000061066

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:27.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61734919.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.14
p-value of test                       :  7.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    4.79
p-value of test                       :  3.6e-3

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.16
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.01
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.62
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.64
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908296
  j =  2                              :            45849
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907927
  j =  2                              :            46035
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.94
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.64
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.39
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.66
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.96
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.29
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.09
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.27
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.53
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.23
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.85
p-value of test                       :  3.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.86
p-value of test                       :    0.9979

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.89
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.66
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.51
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999933668

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.36
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000008206

Normal statistic for number of bits   :   0.065
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:59.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62750727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:19.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.97
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:58.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907759
  j =  2                              :            46116
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908004
  j =  2                              :            45992
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17719.47
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.62
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.36
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.96
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.90
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.90
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.35
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.50
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.28
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.13
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.39
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.51
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.04
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999879227

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.06
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000203392

Normal statistic for number of bits   :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:09.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42795016.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.03
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.41
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4875.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:57.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46361
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870361
  j =  1                              :        399907283
  j =  2                              :            46351
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908679
  j =  2                              :            45653
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.97
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.48
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.46
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.16
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.53
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.17
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.18
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.89
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  464.63
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.57
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.93
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.96
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.42
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.10
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.99
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.86
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000022600

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.52
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999945827

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:22.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44433416.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5550
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:29.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.84
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.16
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5240.70
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907957
  j =  2                              :            46017
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907915
  j =  2                              :            46038
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.83
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.80
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   15.76
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.42
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.35
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.60
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.46
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.56
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.81
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  259.51
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.84
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.39
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.28
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  258.25
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.55
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999964601

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.38
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000111970

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:16.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45416456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.06
p-value of test                       :  8.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.13
p-value of test                       :    0.9995    *****

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.29
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7191.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.17
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.23
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.17
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.04
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908353
  j =  2                              :            45816
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908633
  j =  2                              :            45679
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.20
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.78
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.72
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.92
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.31
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.76
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.45
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.18
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.29
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.76
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.86
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.85
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.94
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4259.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.89
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000016957

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.54
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999856361

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:02.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46399496.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.88
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    4.77
p-value of test                       :  3.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     185
p-value of test                       :  3.2e-3

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.93
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.42
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:56.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46145
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870145
  j =  1                              :        399907718
  j =  2                              :            46129
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908036
  j =  2                              :            45976
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17689.90
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.16
p-value of test                       :    0.9921


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.28
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.19
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.93
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.50
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.85
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.82
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.62
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.68
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.20
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12095.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.63
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000038698

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   97.80
p-value of test                       :  2.5e-4    *****


-----------------------------------------------
Total number of bits:  8000278401

Normal statistic for number of bits   :    2.20
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    2.70
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.43
p-value of test                       :  7.5e-3

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:44.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 102  Run of bits, r = 27             2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47284232.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:11.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.22
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.73
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.87
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908380
  j =  2                              :            45807
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46270
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870270
  j =  1                              :        399907463
  j =  2                              :            46264
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-5
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:27.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.2e-3

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.05
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.41
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.93
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.56
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.97
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.93
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.82
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.23
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.39
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.17
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.38
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.52
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000040063

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.00
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000056047

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:56.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48332808.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5650
p-value of test                       :  1.0e-3


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.76
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:31.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.84
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.48
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908631
  j =  2                              :            45680
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45549
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869549
  j =  1                              :        399908905
  j =  2                              :            45543
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.64
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.92
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.48
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  186.42
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.65
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.91
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.16
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.97
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.47
p-value of test                       :  9.2e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.74
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10218.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4655.15
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3916.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.12
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999796799

Normal statistic for number of bits   :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.07
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999871709

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  4.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    7.18
p-value of test                       :  3.0e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.50
p-value of test                       :    0.9998    *****

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:13.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 105  AutoCor, d=1, r=27              0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49381396.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7112
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.22
p-value of test                       :  2.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    4.65
p-value of test                       :  4.2e-3

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.98
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.81
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.54
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.89
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.12
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908315
  j =  2                              :            45835
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.35e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17511.23
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.84
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.73
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.23
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.67
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.66
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.85
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.93
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.96
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11534.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.63
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999985907

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.29
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000152062

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.46
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:43.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50266132.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    4.98
p-value of test                       :  3.0e-3

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.41
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908464
  j =  2                              :            45762
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908550
  j =  2                              :            45719
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.63
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.08
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.08
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.91
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.42
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.40
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.44
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.26
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10283.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.61
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999945983

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.10
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000040549

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.19
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:54.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51347476.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.05
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1519.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6857.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.92
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:58.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908374
  j =  2                              :            45810
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908334
  j =  2                              :            45827
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.85
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17566.61
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.90
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   64.17
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.25
p-value of test                       :  8.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.04
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.75
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.13
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.10
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.26
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.20
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.04
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.08
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.60
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:33.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.74
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000028282

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.80
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000175030

Normal statistic for number of bits   :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:38.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52428820.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    3.17
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    4.97
p-value of test                       :  3.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     183
p-value of test                       :  5.0e-3

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.32
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:29.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.08
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.06
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907962
  j =  2                              :            46016
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908337
  j =  2                              :            45827
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.98e-4
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17037.59
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.32
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.90
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.35
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.65
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.22
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.20
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.64
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.80
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    2.58
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:34.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.98
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000036934

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.42
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999886205

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:54.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53575700.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.00
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.98
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908341
  j =  2                              :            45825
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907769
  j =  2                              :            46108
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.35
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17690.60
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.58
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.04
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.96
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.09
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.97
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.97
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.040
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.94
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.57
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999883157

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.15
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000147160

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.067
p-value of test                       :    0.53

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    2.99
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:20.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54558740.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:46.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.61
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.39
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.65
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.54
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907776
  j =  2                              :            46112
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908301
  j =  2                              :            45842
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.032
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.85
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.20
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.31
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.22
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.32
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.01
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.67
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.29
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.06
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000076093

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.74
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999971120

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.03

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:46.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16               0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55476244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7113
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7270.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.77
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4885.52
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:00.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46262
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870262
  j =  1                              :        399907481
  j =  2                              :            46252
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908316
  j =  2                              :            45842
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-6
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.64e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.03
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.18
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.58
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.43
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.94
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5225.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.59
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.80
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.90
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 4.54e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.59
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999866660

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999972803

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:56.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56852500.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5558
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4162
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.48
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.55
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908516
  j =  2                              :            45739
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908302
  j =  2                              :            45849
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9969


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17601.11
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.12
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.39
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.54
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.24
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.42
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999974966

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.93
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999885869

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:21.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57901076.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7599
p-value of test                       :  5.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.27
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:28.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.92
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:59.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908221
  j =  2                              :            45879
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907912
  j =  2                              :            46041
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9939


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.55
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.20
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17517.09
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.99
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.38
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.99
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.35
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.96
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.85
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.00
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.14
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.68
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.28
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.23
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.60
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.08
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.63
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.79
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999996845

Normal statistic for number of bits   :  -0.025
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.13
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999911525

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:52.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 18  BirthdaySpacings, t = 8         5.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59015188.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:46.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.24
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:18.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:29.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.79
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.29
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908706
  j =  2                              :            45647
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46274
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870274
  j =  1                              :        399907453
  j =  2                              :            46272
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -4.15e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.54
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.25
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.38
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.81
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.73
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.08
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.52
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.81
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.38
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    3.35
p-value of test                       :  4.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.51
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.01
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999926807

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.58
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999942857

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

Tests on the sum of all N observations
Standardized normal statistic         :   0.090
p-value of test                       :    0.46

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:49.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60325908.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.27
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.39
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.49
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.74
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.32
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907971
  j =  2                              :            46013
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 3.32e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.54e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.38
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9989

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.64
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.68
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.03
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.26
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.95
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.79
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.30
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.08
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.75
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.26
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999926942

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.18
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999879095

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:38.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61243412.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.17
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9911

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1568.78
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6819.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:21.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.18
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.17
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.73
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45627
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869627
  j =  1                              :        399908748
  j =  2                              :            45623
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.60e-4
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    : 5.04e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17164.05
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.32
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.06
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4830.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.91
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.57
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.93
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.82
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.90
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.73
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9770.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11468.33
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.79
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000042091

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.64
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000128200

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:58.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62324756.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:28.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.40
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.85
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.56
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.66
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908045
  j =  2                              :            45973
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908724
  j =  2                              :            45635
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.69
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.55
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.51
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.80
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.62
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.19
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.46
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.96
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.74
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10242.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.00
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000114322

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.76
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999950636

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63275028.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.90
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.91
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6910.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.46
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.26
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:20.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908208
  j =  2                              :            45893
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908139
  j =  2                              :            45926
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:28.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.30
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.25
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.31
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.13
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.62
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.36
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.92
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.47
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.20
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.84
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.65
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.91
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.10
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999944876

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.97
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000232591

Normal statistic for number of bits   :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:40.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42827785.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:00:48.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4508
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  187.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7300.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:29.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.09
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.16
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.46
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:59.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908258
  j =  2                              :            45865
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908400
  j =  2                              :            45794
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.87e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 3.38e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:28.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.30
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.08
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.96
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.63
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.42
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.08
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.59
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.47
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.03
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.77
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4795.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.98e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4718.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.77
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999817376

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.10
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000003157

Normal statistic for number of bits   :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:30.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44498953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5534
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1548.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6982.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.46
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.80
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:59.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908014
  j =  2                              :            45981
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908019
  j =  2                              :            45986
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    4.71
p-value of test                       :  4.1e-3


-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17383.19
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.48
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.17
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.83
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.51
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.63
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.88
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.96
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.30
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.23
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.59
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.49
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.11
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999970784

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.76
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999900113

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:04.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45547529.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.74
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7363.91
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.10
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4863.25
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908010
  j =  2                              :            45989
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908649
  j =  2                              :            45674
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.60
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   12.03
p-value of test                       :    0.9999    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.06
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.90
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.16
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.68
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.20
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.63
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.94
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.81
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000115216

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.63
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000010861

Normal statistic for number of bits   :   0.086
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:33.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46465033.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.84
p-value of test                       :  9.3e-5    *****

Anderson-Darling statistic = A2       :    8.17
p-value of test                       :  1.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   66.65
p-value of test                       :  1.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.65
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.01
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.75
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908098
  j =  2                              :            45942
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908515
  j =  2                              :            45735
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.60e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17288.92
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.29
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.67
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.44
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.38
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.25
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.51
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.14
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.35
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.10
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.93
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.68
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.44e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9681.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5104.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11536.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.85
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999952736

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.34
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000222871

Normal statistic for number of bits   :    1.76
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:00.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 38  Run, r = 0                      1.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47513609.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:37.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6922.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45575
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869575
  j =  1                              :        399908857
  j =  2                              :            45561
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908237
  j =  2                              :            45877
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:27.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.92
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.05
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.60
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.39
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.62
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.89
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.48
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.18
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.58
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.36
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12009.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.54
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000128521

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.52
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000128236

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.52
p-value of test                       :  5.8e-3

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:33.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48529417.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.99
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1526.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7336.74
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.37
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.88
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.15
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907991
  j =  2                              :            45997
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908324
  j =  2                              :            45835
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17623.51
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.93
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.82
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.80
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.25
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.11
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.90
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.86
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.76
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.15
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.34
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    5.00
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  254.88
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.90
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999961262

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.12
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000088480

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:59.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49512457.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.84
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.20
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907984
  j =  2                              :            46005
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907944
  j =  2                              :            46022
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.19e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.94
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.68
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.85
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.48
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   92.70
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.56
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.17
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.08
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10275.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10297.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3940.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11532.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.78
p-value of test                       :    0.9900


-----------------------------------------------
Total number of bits:  7999944423

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.66
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000030658

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:17.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 M (L=1000, r=20)    0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50364425.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6890.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:29.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.79
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4873.65
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907920
  j =  2                              :            46034
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46289
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870289
  j =  1                              :        399907428
  j =  2                              :            46277
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17706.12
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.27
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.94
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.54
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.76
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.29
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.80
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.20
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5223.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.44e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.50
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.22
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -2.58e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:38.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.46
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999980915

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.09
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999975968

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:45.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51413001.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.91
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6909.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.99
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4867.18
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45443
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869443
  j =  1                              :        399909118
  j =  2                              :            45435
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908669
  j =  2                              :            45658
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.75e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17521.09
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.04
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.02
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.14
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.16
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.87
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.65
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.85
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.70
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.97e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.05e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.20
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000040066

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.65
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000049525

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.080
p-value of test                       :    0.47

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:04.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52461577.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.85
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     354
p-value of test                       :  1.3e-3

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.04
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.30
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908093
  j =  2                              :            45949
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46262
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870262
  j =  1                              :        399907481
  j =  2                              :            46252
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  9.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    5.30
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.64
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17931.50
p-value of test                       :  3.9e-3



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.83
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.60
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.35
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.26
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.68
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.43
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.88
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999880841

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.83
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000088504

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    2.54
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         : 7.20e-4
p-value of test                       :    0.50

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:49.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53477385.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.67
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:29.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.19
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.46
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908134
  j =  2                              :            45927
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908546
  j =  2                              :            45724
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9948


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.74
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.93
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17601.64
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.76
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.85
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.17
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.73
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.23
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.91
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.89
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.55
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.84
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.45
p-value of test                       :    0.9935

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.60
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999981212

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.49
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999929432

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:03.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54493193.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4514
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7104
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.51
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.92
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.02
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.13
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45525
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869525
  j =  1                              :        399908955
  j =  2                              :            45515
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908189
  j =  2                              :            45901
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.17e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.96
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   67.66
p-value of test                       :  7.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.99
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.08
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.97
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.30
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.46
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.27
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999979196

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.24
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999830570

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:05.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 M (L=50, r=25)      7.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55443465.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1490
p-value of test                       :  4.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334610
  j =  1                              :        599997020
  j =  2                              :             1490
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.88
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.28
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:02:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.70
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.02
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:58.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908595
  j =  2                              :            45698
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908606
  j =  2                              :            45694
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-4
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.79e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17697.60
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.88
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.91
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.49
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.63
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.00
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.36
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11495.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.66
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000049270

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.53
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999872738

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:11.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           4.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56426505.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:29.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.13
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5178.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907839
  j =  2                              :            46079
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908147
  j =  2                              :            45919
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.82
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.23
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.50
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.29
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.05
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.22
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.36
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10317.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.20
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000048163

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000120196

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:51.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57475081.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    4.76
p-value of test                       :  3.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9977

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.16
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:02.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908549
  j =  2                              :            45715
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46289
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870289
  j =  1                              :        399907424
  j =  2                              :            46285
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.93
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17748.45
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.34
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.62
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.56
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.11
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.45
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.77
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.53
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.31
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.94
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.07
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.65
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.3e-3

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10282.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.14
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.18
p-value of test                       :  9.8e-3


-----------------------------------------------
Total number of bits:  8000330691

Normal statistic for number of bits   :    2.61
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.21
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000107848

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:08.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58523657.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.3e-3


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5607
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:16.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.96
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.70
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  502.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7270.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.82
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907746
  j =  2                              :            46121
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45571
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869571
  j =  1                              :        399908864
  j =  2                              :            45559
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.03
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17145.22
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.45
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.19
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.68
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.19
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.63
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.46
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.42
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.01
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.18
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.51
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000122815

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.25
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999997406

Normal statistic for number of bits   :  -0.021
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:24.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59572233.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:02:37.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    3.00
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.10
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5238.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907892
  j =  2                              :            46045
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46583
p-value of test                       :  5.3e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870583
  j =  1                              :        399906835
  j =  2                              :            46581
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.80
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.86
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.58
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.41
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.83
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5244.30
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.29
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.58
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.01
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9923

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.64
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:30.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.18
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.52
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999794201

Normal statistic for number of bits   :   -1.63
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.01
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000043888

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:44.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 45  CollisionPermut, r = 10         5.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60620809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    4.22
p-value of test                       :  6.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     826
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9963

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.13
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.90
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907963
  j =  2                              :            46011
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908185
  j =  2                              :            45906
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:30.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.55
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   49.07
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.24
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.55
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.80
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.84
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.12
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.77
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.09
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:30.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5068.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.88
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000019858

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.06
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999904712

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61669385.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:21.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.82
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.44
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908329
  j =  2                              :            45831
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908033
  j =  2                              :            45982
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.81e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:12.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:12.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.40
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.30
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.50
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.76
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.25
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.99
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.44
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.58
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.88
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.16
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.49
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.31
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:03:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.76
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000072163

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.61
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999936296

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:48.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62685193.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    3.43
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  368.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:28.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.13
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.63
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908141
  j =  2                              :            45922
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45472
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869472
  j =  1                              :        399909058
  j =  2                              :            45468
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.16
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17682.42
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.85
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.79
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.73
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.93
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.11
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.06
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.18
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.28
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.95
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.31
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9627.99
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.84
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:03:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.18
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.85
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999970001

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.48
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000102343

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.21
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:57.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42860554.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    3.16
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.36
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:48.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908614
  j =  2                              :            45687
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908092
  j =  2                              :            45945
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.22e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.11e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:28.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.99
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.33
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.31
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.79
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.28
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5184.45
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.46
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.96
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.98
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.65e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.58
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.16
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  261.13
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.67
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 2.72e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.51
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000027154

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.73
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999996473

Normal statistic for number of bits   :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:47.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43810831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    4.56
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    3.48
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:36.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.80
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907619
  j =  2                              :            46186
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908448
  j =  2                              :            45773
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.09e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.30
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.24
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.06
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.99
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.54
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.82
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.64
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.41
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.29
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.70
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.90
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11318.95
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.04
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000069967

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.35
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999957035

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:10.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 100  HammingIndep, L=1200, r=25      0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44695567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5521
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1540.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:35.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.52
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908823
  j =  2                              :            45581
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908095
  j =  2                              :            45945
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.23
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.66
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.92
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.72
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.96
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  312.34
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.00
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.96
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5202.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.77
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.24
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.91
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.60
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:37.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.04
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000049072

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.56
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000022816

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:22.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45711375.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1230
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334350
  j =  1                              :        599997540
  j =  2                              :             1230
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.99
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.27
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908649
  j =  2                              :            45668
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907810
  j =  2                              :            46089
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.72
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17335.85
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.40
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.15
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.68
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.63
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.60
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4796.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.86
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.29
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.97
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.98
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.37
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000035311

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.07
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000149452

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:58.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46792719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9945


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4496
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.79
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.89
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:02.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46137
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870137
  j =  1                              :        399907733
  j =  2                              :            46123
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45544
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869544
  j =  1                              :        399908916
  j =  2                              :            45536
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.38
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  599.56
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.32
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.84
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.82
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.19
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  253.93
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.97
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.81
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.43
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.89
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999997895

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.01
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000158770

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:51.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47808527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4500
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.54
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.38
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.81
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.93
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907962
  j =  2                              :            46010
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907898
  j =  2                              :            46045
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.51e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.95
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.99
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.19
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.10
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.79
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.13
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.02
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.84
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.42
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.55e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.91
p-value of test                       :    0.9988

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.77
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000086560

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.48
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000061945

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.067
p-value of test                       :    0.53

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:20.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48857103.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1479
p-value of test                       :  1.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334599
  j =  1                              :        599997042
  j =  2                              :             1479
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     544
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.11
p-value of test                       :    0.9999    *****

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.37
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.17
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:30.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.83
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:09.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908540
  j =  2                              :            45727
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908338
  j =  2                              :            45825
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:46.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.35
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.66
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.78
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.73
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.36
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.93
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.53
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.35
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.41
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.18
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.00
p-value of test                       :  3.4e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:31.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.59
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999907907

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.67
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000144553

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:20.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49905679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.00
p-value of test                       :  8.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   94.00
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.63
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.22
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908559
  j =  2                              :            45716
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908455
  j =  2                              :            45765
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.32e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:19.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.88
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   46.22
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.71
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.45
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.20
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.72
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.94
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.77
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.75
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.90
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.94
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.07
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:25.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.24
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000057400

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.23
p-value of test                       :  4.3e-3


-----------------------------------------------
Total number of bits:  7999731870

Normal statistic for number of bits   :   -2.12
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:16.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50954255.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:33.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:35.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:11.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  297.66
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:20.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.08
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.50
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907857
  j =  2                              :            46067
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908148
  j =  2                              :            45923
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:29.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.74
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.85
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.77
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.98
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.30
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.71
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.18
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.92
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.41
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.69
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.39
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.15
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.02
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:27.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.71
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999831515

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.99
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000047761

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.12
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:15.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52002831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.73
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.95
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45690
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869690
  j =  1                              :        399908623
  j =  2                              :            45684
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908082
  j =  2                              :            45956
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.05e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:19.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:12.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:29.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17180.47
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.28
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.79
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.24
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.26
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.06
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.10
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.88
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11637.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.81
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999922163

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.86
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999945959

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:37.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53051407.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4497
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9964

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    3.81
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:19.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.27
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4865.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908300
  j =  2                              :            45847
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45540
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869540
  j =  1                              :        399908924
  j =  2                              :            45532
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:12.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:28.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:28.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.02
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.22
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.81
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.81
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.86
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.44
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.90
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.43
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.74
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.86e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.11
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.94
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.85
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000013423

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.02
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999980780

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:09.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54099983.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4523
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.70
p-value of test                       :  4.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5018.45
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45540
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869540
  j =  1                              :        399908922
  j =  2                              :            45536
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908479
  j =  2                              :            45756
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.38
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:29.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17210.41
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.75
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.17
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.54
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.92
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.06
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.40
p-value of test                       :    0.9900


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.01
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.85
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:43.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.73
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.48
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999983441

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.55
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000055993

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :  1.4e-4    *****

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  3.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.56
p-value of test                       :  5.2e-3

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:46.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55148559.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4206
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9962

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5173.61
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908087
  j =  2                              :            45955
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45585
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869585
  j =  1                              :        399908833
  j =  2                              :            45579
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.34
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.52
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.06
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5170.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.62
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.63
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.00
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.95
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.24e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.10
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.78
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:03:51.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.97
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.95
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999994511

Normal statistic for number of bits   :  -0.043
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.65
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999858779

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:05.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56197135.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.07
p-value of test                       :  8.5e-3

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.19
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4841.02
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908654
  j =  2                              :            45667
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908099
  j =  2                              :            45949
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.53
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.90
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.06
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.40
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.43
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.07
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5184.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.38
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.85
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.05
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.83
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9788.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10255.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11610.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11388.22
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.28
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000087529

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000171325

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.24
p-value of test                       :    0.01

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:23.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57245711.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    6.34
p-value of test                       :  6.9e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  491.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7199.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.78
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.98
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5218.95
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:59.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908074
  j =  2                              :            45957
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908497
  j =  2                              :            45747
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.61e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.69e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17370.73
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.06
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.01
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.17
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.37
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.25
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.71
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.88
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.53
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.12
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.88
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.89
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3824.62
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.90
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000065713

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.48
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000009319

Normal statistic for number of bits   :   0.074
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

Tests on the sum of all N observations
Standardized normal statistic         : -4.28e-3
p-value of test                       :    0.50

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:50.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         6.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 98  HammingIndep, L=300, r=26       0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58294287.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.54
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:49.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.32
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.12
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.49
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907805
  j =  2                              :            46084
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908354
  j =  2                              :            45820
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.32
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.54
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.89
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.87
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.00
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.17
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.68
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.81
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.10
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.26
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.97
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999903143

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.06
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999891503

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:32.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59342863.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9963

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.84
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7265.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.04
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908008
  j =  2                              :            45993
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908707
  j =  2                              :            45639
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.69
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.09
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.13
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.59
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.75
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.58
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.12
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.83
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.47
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :1.40e-16
p-value of test                       :    0.50

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.17
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.20
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.33
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10266.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.60
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.00
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000016225

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.86
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000089230

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:06.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60391439.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7076
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    4.08
p-value of test                       :  7.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9930

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:47.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.51
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.42
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.88
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908155
  j =  2                              :            45912
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908828
  j =  2                              :            45574
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.46
p-value of test                       :  2.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.78
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.80
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.81
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.07
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5200.59
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.92
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.16
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.83
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.87
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4678.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.36
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999968138

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.33
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999776756

Normal statistic for number of bits   :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:58.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               2.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61440015.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5691
p-value of test                       :  1.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    3.54
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.60
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.92
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.48
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907979
  j =  2                              :            45997
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908295
  j =  2                              :            45851
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.51e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  102.66
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.59
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.57
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.13
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.40
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.84
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.40
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.50
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12275.92
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.69
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999977246

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.17
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999905915

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:36:58.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         1.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62488591.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.63
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.23
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908332
  j =  2                              :            45825
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908276
  j =  2                              :            45856
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.06e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.00
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.13
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.39
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.78
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.44
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.34
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.47
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.03
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.42
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.65
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.80
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:31.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3922.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.37
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999917009

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.09
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999976973

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.023
p-value of test                       :    0.49

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:14.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42893323.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7565
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.21
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:30.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.43
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5198.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45360
p-value of test                       :    0.9924


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869360
  j =  1                              :        399909281
  j =  2                              :            45358
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908365
  j =  2                              :            45816
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.60
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.32
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.95
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.97
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.71
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.93
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.81
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.83
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.51
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.61
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.88
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.58
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.27
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.66e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.46
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.18
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.42
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.28
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999898394

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.41
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999962768

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:36.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43909131.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7527
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.17
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:53.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908437
  j =  2                              :            45777
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908512
  j =  2                              :            45741
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:28.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.82
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.37
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.83
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.87
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.91
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.54
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.14
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.45
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.24
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9713.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3917.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.54
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000001048

Normal statistic for number of bits   : 8.29e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000099934

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:18.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45023243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    3.03
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:37.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.68
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4821.48
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:52.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907904
  j =  2                              :            46036
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908078
  j =  2                              :            45952
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:27.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.30
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.01
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.85
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.45
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.50
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.61
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.38
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.53
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.84
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.27
p-value of test                       :    0.9989


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.45
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9752.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:32.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.77
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999884297

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.54
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999882209

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:56.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46202891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9956

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7228.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.54
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907862
  j =  2                              :            46063
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908149
  j =  2                              :            45921
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.54
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.06
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.29
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.04
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.10
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.17
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.88
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.02
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.86
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.99
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.02
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.59
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.67
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.21
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999842558

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.06
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000121231

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:34.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47054849.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5589
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.48
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.61
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7155.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.28
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.57
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.79
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908212
  j =  2                              :            45891
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907949
  j =  2                              :            46021
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   36.48
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:27.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    4.77
p-value of test                       :  3.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   70.00
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.070
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    4.37
p-value of test                       :  6.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16949.71
p-value of test                       :    0.9952



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.15
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.78
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.86
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.88
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.59
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.99
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.83
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9777.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.46
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.20
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.31
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000091894

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.94
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000117265

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:49.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48005121.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7537
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     979
p-value of test                       :  4.9e-3

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.34
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.87
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.00
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:57.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908419
  j =  2                              :            45789
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908094
  j =  2                              :            45950
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.79e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.78
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17379.88
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.55
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.99
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.47
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.44
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.44
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.83
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.14
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.25
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999924977

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.59
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000016108

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    2.46
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:38.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49119233.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5198
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     341
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.45
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.63
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.58
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.14
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908295
  j =  2                              :            45848
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908337
  j =  2                              :            45827
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.27
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.02
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.81
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.53
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.62
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.34
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.74
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.51
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.30
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.03
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.04
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.50
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.42
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.07
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000062374

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.70
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999945392

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:01.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50298881.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.28
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.28
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.11
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:52.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907985
  j =  2                              :            46003
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907791
  j =  2                              :            46094
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-4
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    : 1.53e-5
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.54
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.02
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.85
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.56
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.44
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.33
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.53
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5256.77
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.13
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.36
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.98
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.04
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5117.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.90
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.25
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999930665

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.53
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000000715

Normal statistic for number of bits   : 5.65e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.017
p-value of test                       :    0.51

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:04.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51216385.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:15.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.70
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.94
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.04
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:49.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908576
  j =  2                              :            45709
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45354
p-value of test                       :    0.9930


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869354
  j =  1                              :        399909294
  j =  2                              :            45350
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9953


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.61
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17225.16
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.97
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.04
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.63
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.49
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.97
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.33
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.21
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.05
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9804.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4686.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.16
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000100237

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.82
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999960221

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         : -9.20e-4
p-value of test                       :    0.50

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:07.48
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52297729.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    6.72
p-value of test                       :  4.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.35
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46266
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870266
  j =  1                              :        399907472
  j =  2                              :            46258
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46349
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870349
  j =  1                              :        399907305
  j =  2                              :            46343
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.38
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.23
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.22
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.44
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.14
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.82
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.27
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.30
p-value of test                       :  9.7e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.87
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.28
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.21
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.60
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000003631

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.08
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999940472

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.048
p-value of test                       :    0.48

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.041
p-value of test                       :    0.52

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:15.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2S, t = 3         4.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53346305.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.02
p-value of test                       :  9.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.99
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.20
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.49
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:18.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45597
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869597
  j =  1                              :        399908806
  j =  2                              :            45597
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45627
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869627
  j =  1                              :        399908751
  j =  2                              :            45617
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17254.14
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.58
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.16
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.27
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.57
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  310.82
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.30
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.32
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.92e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10269.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.11
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000078004

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.79
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999984143

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:51.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54394881.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4169
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  291.16
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.88
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4834.94
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:59.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908214
  j =  2                              :            45890
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908457
  j =  2                              :            45767
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.25e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.53
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.18
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.84
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.44
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.91
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.17
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.81
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.11
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.63
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.69
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.69
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 4.10e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.57
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4714.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.34
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.49
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999985415

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.92
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999882656

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:41.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55508993.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9922

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  190.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.66
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.12
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:57.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907780
  j =  2                              :            46107
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45597
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869597
  j =  1                              :        399908808
  j =  2                              :            45593
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.03
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.08
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.89
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.80
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.10
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.17
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  575.19
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.41
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.05
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  296.93
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  253.52
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.98
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.91e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.99
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3889.55
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.42
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.64
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000019642

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.02
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999993443

Normal statistic for number of bits   :  -0.052
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:09.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56524801.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1167
p-value of test                       : 1 -  2.4e-8    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334287
  j =  1                              :        599997666
  j =  2                              :             1167
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  342.28
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.17
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.60
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908387
  j =  2                              :            45802
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908535
  j =  2                              :            45722
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 4.46e-4
p-value of test                       :  3.6e-4    *****

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.65
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.61
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.84
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.94
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.78
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.20
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9696.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.60
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000091504

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.78
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999924374

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         : 5.44e-3
p-value of test                       :    0.50

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:22.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  2.4e-8
 35  Gap, r = 25                     0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57573377.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7203.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.60
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.41
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908242
  j =  2                              :            45873
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908256
  j =  2                              :            45869
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.63
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.98
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.47
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.47
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.77
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.87
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.19
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.85
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.53
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -403.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000074149

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.55
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999898544

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:21.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58687489.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.43
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4926.08
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908812
  j =  2                              :            45594
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908007
  j =  2                              :            45986
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.61
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.54e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17027.92
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.07
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.32
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.50
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.13
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.86
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.72
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.08
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.40
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.09
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999982031

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.02
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000010594

Normal statistic for number of bits   :   0.084
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:33.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59867137.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  184.12
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6897.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.61
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4892.20
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908363
  j =  2                              :            45811
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908348
  j =  2                              :            45820
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.94e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.94
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17692.99
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.57
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.64
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.21
p-value of test                       :  9.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.83
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.10
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.11
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.19
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.34
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:31.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.81
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999900830

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.54
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999939209

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:22.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61014017.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7516
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7211.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.95
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.66
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908267
  j =  2                              :            45862
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908987
  j =  2                              :            45502
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.00e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17802.21
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.49
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.83
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.73
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.89
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.83
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.36
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.54
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.73
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.52
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.64
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.05
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:32.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3956.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.52
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999998687

Normal statistic for number of bits   :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.28
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999908507

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:28.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61898753.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4470
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7544
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.81
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908241
  j =  2                              :            45875
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908828
  j =  2                              :            45580
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.52
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.47
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.31
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.93
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.07
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.96
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.14
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  316.77
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.81
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.68
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -401.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.21
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:27.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.94
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000174319

Normal statistic for number of bits   :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.40
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999941609

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:39.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62947329.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.79
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.01
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1317.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.30
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.72
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:58.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908704
  j =  2                              :            45645
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908465
  j =  2                              :            45763
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.89
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:29.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.91
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.29
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.34
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.03
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.71
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.68
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.23
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.90
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.19
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.32
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.56
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.04
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999810146

Normal statistic for number of bits   :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.43
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000047962

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:51.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42926092.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5550
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:29.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.37
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.06
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:59.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908426
  j =  2                              :            45778
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908496
  j =  2                              :            45752
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.05e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.59
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.04
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.73
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.49
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.50
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.79
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.37
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.58
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.06
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.48
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12039.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.14
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999913631

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.60
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000040915

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:22.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44236812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1499
p-value of test                       :  1.7e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334619
  j =  1                              :        599997002
  j =  2                              :             1499
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    4.27
p-value of test                       :  6.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9908

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.64
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.65
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:59.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908090
  j =  2                              :            45949
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908045
  j =  2                              :            45976
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    : 3.34e-5
p-value of test                       : 1 -  3.3e-5    *****

Anderson-Darling statistic = A2       :    4.68
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17163.26
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.40
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.64
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.81
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.44
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.39
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.73
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.37
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.49
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.94
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.35
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.08
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.45
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000080125

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.48
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999968174

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:11.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           1.7e-4
 48  MaxOft, t = 24                  0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45318156.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997293
  j =  2                              :             1352
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.15
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.45
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908764
  j =  2                              :            45612
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907697
  j =  2                              :            46147
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-5
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.75
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.52
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.63
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.31
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.85
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.11
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.11
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.42
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.50
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.19
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.16
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.81
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.21
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.19
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.95
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12040.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.81
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000000430

Normal statistic for number of bits   : 3.40e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.74
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999993131

Normal statistic for number of bits   :  -0.054
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:53.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46301196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.03
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.19
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.07
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908035
  j =  2                              :            45978
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45274
p-value of test                       :    0.9977


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869274
  j =  1                              :        399909460
  j =  2                              :            45258
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.58e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.43
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.42
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9982

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.08
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.56
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.05
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.04
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.65
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.73
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  463.26
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.30
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.36
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.96
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.87
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9720.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.97
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000136195

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.80
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000059803

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.22
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:42.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47480848.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    3.71
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.31
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.38
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46144
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870144
  j =  1                              :        399907717
  j =  2                              :            46134
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45639
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869639
  j =  1                              :        399908725
  j =  2                              :            45633
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.96e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.03
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.13
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.59
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.46
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.73
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.00
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.06
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.23
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.34e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.39
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10367.28
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.16
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.50
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000062551

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.92
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999969035

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:36.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48398352.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4144
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.18
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.84
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907946
  j =  2                              :            46021
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908540
  j =  2                              :            45724
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:27.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17236.36
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.46
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.67
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.87
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.41
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.58
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.84
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.71
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.83
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10316.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.52
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:38.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12157.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.05
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000080389

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.94
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999978821

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:37.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49414160.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7051
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    3.90
p-value of test                       :  9.7e-3

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.78
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.81
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907928
  j =  2                              :            46030
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45458
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869458
  j =  1                              :        399909085
  j =  2                              :            45456
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.43
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17746.22
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.33
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.02
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.80
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.82
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.96
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.49
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.88
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.23
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.46
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.71
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.60
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.87
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9747.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.02
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.52
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000073339

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.92
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000028765

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:57.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 18  BirthdaySpacings, t = 8         0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50561040.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4832.94
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908859
  j =  2                              :            45566
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908611
  j =  2                              :            45687
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.05
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17138.86
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.74
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.19
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.10
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.16
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.71
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.87
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.06
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.33
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.88
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.04
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:35.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4742.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.02
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999926138

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.19
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999992864

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    2.41
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:19.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51707920.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9992    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7026.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.37
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.10
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46018
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870018
  j =  1                              :        399907971
  j =  2                              :            46004
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908021
  j =  2                              :            45988
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  9.9e-4    *****

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-4
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    : 6.43e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.38
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.55
p-value of test                       :  7.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.32
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.81
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.74
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.87
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.10
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.96
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.24
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.72
p-value of test                       :    0.9972


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.59
p-value of test                       :  4.8e-3

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.34
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10229.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.02
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999920528

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.80
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999864857

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:01.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52658192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1547.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.77
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.89
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908282
  j =  2                              :            45859
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908450
  j =  2                              :            45772
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   67.74
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.41
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.63
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.97
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.82
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.62
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.02
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.54
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.05
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000051313

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.49
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999877100

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:21.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53739536.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7094
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.95
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.64
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.28
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908773
  j =  2                              :            45609
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907951
  j =  2                              :            46020
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.52e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.87e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.12
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.89
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.73
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.30
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.75
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.58
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.77
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  310.28
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.31
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.65
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.43
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999932141

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.56
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999893411

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:57.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54820880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5236
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.08
p-value of test                       :  8.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1331.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6850.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.86
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4891.98
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46080
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870080
  j =  1                              :        399907845
  j =  2                              :            46070
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908309
  j =  2                              :            45835
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    6.25
p-value of test                       :  7.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.50
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.13
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.10
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.01
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.39
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.20
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4825.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.37
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.33
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.35
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.38
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000123646

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.24
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000015769

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:32.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               7.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55771152.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7367.24
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:29.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.99
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.54
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46164
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870164
  j =  1                              :        399907675
  j =  2                              :            46158
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908082
  j =  2                              :            45953
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.79
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.66
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.78
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.99
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.00
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.45
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.92
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.76
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.90
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.90
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.95
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.03
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   29.67
p-value of test                       :    0.9971


-----------------------------------------------
Total number of bits:  8000042679

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.11
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000138199

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:22.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56655888.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1483
p-value of test                       :  7.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334603
  j =  1                              :        599997034
  j =  2                              :             1483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.60
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:28.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.47
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46244
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870244
  j =  1                              :        399907516
  j =  2                              :            46236
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908382
  j =  2                              :            45806
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.29
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.75
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.67
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.59
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.46
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.71
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.86
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.16
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.79
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10292.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.36
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999958181

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.79
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999877085

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:15.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            7.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57770000.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.27
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1539.36
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.98
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.15
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.97
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908836
  j =  2                              :            45582
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907757
  j =  2                              :            46117
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-4
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    : 9.85e-6
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17718.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.93
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.82
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.78
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.50
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.08
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.89
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.31
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.45
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.24
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.54
p-value of test                       :  4.0e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.54
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999881222

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.37
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999999110

Normal statistic for number of bits   : -7.04e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:16.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58851344.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.14
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.30
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908541
  j =  2                              :            45728
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907658
  j =  2                              :            46162
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-5
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    : 3.64e-4
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    5.53
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.99
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17580.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.78
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.59
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  113.85
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.07
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.33
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.70
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.26
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -401.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.34
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.26e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.36
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.36
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12060.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.12
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000119149

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.58
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000035656

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:59.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59736080.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.99
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.66
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46364
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870364
  j =  1                              :        399907275
  j =  2                              :            46358
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.13e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.75
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.55
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.19
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.15
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.81
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.53
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.71
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4765.25
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.38
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.49
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.28
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.95
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.23
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.35
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5067.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.91
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000215407

Normal statistic for number of bits   :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.71
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999962189

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:49.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60751888.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    4.05
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7319.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.12
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.91
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5201.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908355
  j =  2                              :            45815
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908528
  j =  2                              :            45733
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17560.78
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.44
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.39
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.10
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.71
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.68
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.98
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.09
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.12
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.61
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.85
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.51
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999952364

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.68
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000004825

Normal statistic for number of bits   :   0.038
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:13.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61833232.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.83
p-value of test                       :  1.3e-3

Test on the Nm values of W_{n,i}(mNP1):    2.36
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.98
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:07.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907824
  j =  2                              :            46079
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46298
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870298
  j =  1                              :        399907407
  j =  2                              :            46292
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.18
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.13
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.42
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.86
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.25
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.58
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.81
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.24
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.40
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.07
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.49
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.72
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.44
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.88
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:26.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.72
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000052597

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.32
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999995495

Normal statistic for number of bits   :  -0.036
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.051
p-value of test                       :    0.52

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:41.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62914576.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.99
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.84
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4883.60
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908118
  j =  2                              :            45935
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908627
  j =  2                              :            45679
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.99e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.57
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.48
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.15
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.43
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.06
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.82
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.69
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.57
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.84
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.68
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.54
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.93
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12021.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.56
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999960797

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.64
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999840824

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.023
p-value of test                       :    0.49

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:49.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42958861.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:18.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.48
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.67
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.61
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908413
  j =  2                              :            45786
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45629
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869629
  j =  1                              :        399908746
  j =  2                              :            45621
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.27
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.24
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.56
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.78
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.27
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.48
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.49
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.15
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.88
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.99
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.43
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.43
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12118.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.97
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999924902

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.11
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999879530

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:39.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44564493.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    6999
p-value of test                       : 1 -  8.7e-5    *****


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.38
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.18
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908207
  j =  2                              :            45892
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908299
  j =  2                              :            45843
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17509.99
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.91
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.44
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.87
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.78
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.11
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.99
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.62
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.57
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.14
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:31.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.23
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.79
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:35.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.33
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.99
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000066697

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.60
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000032383

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:30.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 19  BirthdaySpacings, t = 8        1 -  8.7e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45613069.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1232
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334352
  j =  1                              :        599997536
  j =  2                              :             1232
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7076
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.46
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  342.81
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.33
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.13
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.40
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908299
  j =  2                              :            45846
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908756
  j =  2                              :            45613
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:28.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17430.89
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.59
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.32
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.56
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.85
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.38
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.11
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.85
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.12
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.33
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -403.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.30
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.87
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999921200

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.09
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000069574

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    2.43
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:44.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            0.9999 
 35  Gap, r = 25                     0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46596109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997073
  j =  2                              :             1462
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.10
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.86
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.37
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46252
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870252
  j =  1                              :        399907501
  j =  2                              :            46242
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908305
  j =  2                              :            45840
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.48
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.17
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.00
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.44
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.47
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.14
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.55
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.97
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.28
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.40
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10264.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.92
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11521.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.98
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999964232

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.54
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000024064

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         : 8.20e-4
p-value of test                       :    0.50

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:51.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47579149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.73
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.79
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4900.83
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908286
  j =  2                              :            45845
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46250
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870250
  j =  1                              :        399907505
  j =  2                              :            46240
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.28e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.30e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    6.37
p-value of test                       :  7.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16748.55
p-value of test                       :    0.9999    *****



-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.73
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.56
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.69
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.64
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.83
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.98
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.37
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.25
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.21
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.30
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.18
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.18
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.66
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.22
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000029758

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.79
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999911456

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:35.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 73  GCD                             0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48562189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   89.13
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.48
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908508
  j =  2                              :            45743
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908441
  j =  2                              :            45775
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  6.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17742.88
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.80
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.94
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.83
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5203.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.04
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.75
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.34e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.93
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12074.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.78
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000040042

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.39
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000021214

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:28.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49610765.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.67
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.62
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:00.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908547
  j =  2                              :            45716
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907934
  j =  2                              :            46030
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    7.93
p-value of test                       :  1.4e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   88.89
p-value of test                       :  1.4e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17669.17
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.67
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.12
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.00
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.46
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.97
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.61
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.76
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.23
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.63
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.96
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.68e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.85
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.84
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000067105

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.78
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000125542

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:47.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          1.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50626573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    4.14
p-value of test                       :  7.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.18
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.55
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.13
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4890.05
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46203
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870203
  j =  1                              :        399907598
  j =  2                              :            46195
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46164
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870164
  j =  1                              :        399907673
  j =  2                              :            46162
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.11e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.17
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17211.84
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.00
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.68
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.07
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.74
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.08
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.70
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.03
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.32
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.29
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.99
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.17
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:33.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.93
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.57
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000005557

Normal statistic for number of bits   :   0.044
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.02
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000025120

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:17.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51511309.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    3.08
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9951

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1545.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.50
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.29
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907947
  j =  2                              :            46019
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45517
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869517
  j =  1                              :        399908971
  j =  2                              :            45507
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.47
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.65
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17732.16
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.24
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.48
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.63
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.09
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.06
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.76
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.68
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.23
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.07
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.09
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.14
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.89
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    6.95
p-value of test                       :  3.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  277.57
p-value of test                       :  2.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5119.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.20
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.18
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000032743

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.34
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999963206

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:48.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 88  PeriodsInStrings, r = 0         2.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52527117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.83
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.90
p-value of test                       :  1.2e-5    *****

Anderson-Darling statistic = A2       :    7.47
p-value of test                       :  2.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   57.45
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.87
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4841.11
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908587
  j =  2                              :            45702
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908372
  j =  2                              :            45811
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.31
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.70
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.47
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.92
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.94
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.06
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.91
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.23
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.52
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.24
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  253.92
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10310.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.06
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999914345

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.86
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999956042

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:59.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53772301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.55
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:27.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.36
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907927
  j =  2                              :            46032
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45390
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869390
  j =  1                              :        399909224
  j =  2                              :            45382
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.38
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.01
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.26
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.51
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.81
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.35
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9707.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:32.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11494.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.74
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999863612

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.10
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999879746

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:05.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54788109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7564
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.32
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9946

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.53
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.86
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.17
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46210
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870210
  j =  1                              :        399907583
  j =  2                              :            46204
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907938
  j =  2                              :            46025
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.43e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.31
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.02
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.54
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.91
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.15
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.52
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.63
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.60
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.02
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.19
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.43
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.30
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.20
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.06
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000013264

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.68
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000027961

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:40.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55738381.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1226
p-value of test                       : 1 -  7.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334346
  j =  1                              :        599997548
  j =  2                              :             1226
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5564
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.23
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907898
  j =  2                              :            46048
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907893
  j =  2                              :            46049
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   75.24
p-value of test                       :  2.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17135.39
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.05
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.98
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.94
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.20
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.06
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.41
p-value of test                       :  4.8e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.25e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.31
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000120403

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.72
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999990965

Normal statistic for number of bits   :  -0.071
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.58e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.27
p-value of test                       :    0.01

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.65
p-value of test                       :  4.0e-3

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:19.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  7.5e-5
 64  WeightDistrib, r = 26           2.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56688653.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.77
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.12
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:53.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908817
  j =  2                              :            45587
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908411
  j =  2                              :            45790
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.1e-3


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.55e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17074.31
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.83
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.48
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.55
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.22
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.30
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.17
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.76
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000046714

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   92.85
p-value of test                       :  8.0e-4    *****


-----------------------------------------------
Total number of bits:  7999918893

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:55.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 102  Run of bits, r = 27             8.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57802765.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9947

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.44
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  376.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6847.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.26
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.22
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907796
  j =  2                              :            46096
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46190
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870190
  j =  1                              :        399907626
  j =  2                              :            46178
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    5.11
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   74.42
p-value of test                       :  7.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   16.82
p-value of test                       :  7.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.77
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.63
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.58
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.29
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  302.61
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.38
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.45
p-value of test                       :  4.8e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.31
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.80
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.49
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.73
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000042079

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.69
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000046993

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:43.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           7.7e-4
 69  MatrixRank, L=1000, r=26        7.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58654733.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:28.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.06
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.50
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908309
  j =  2                              :            45838
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907904
  j =  2                              :            46042
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.59
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.16
p-value of test                       :  8.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.59
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.67
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.61
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.92
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.67
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.70
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.82
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 7.65e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.23
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.48
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999930335

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.66
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000063961

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:41.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59932685.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4206
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.94
p-value of test                       :  3.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:11.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:29.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.52
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.42
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4891.99
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908792
  j =  2                              :            45598
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45640
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869640
  j =  1                              :        399908722
  j =  2                              :            45636
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.03
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.78
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.97
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.31
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.90
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.83
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.61
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.25
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.72
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.03
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.59
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.13
p-value of test                       :    0.9966


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.18
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.34
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.86
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999797132

Normal statistic for number of bits   :   -1.60
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.47
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000108124

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:25.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60817421.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    6998
p-value of test                       : 1 -  8.3e-5    *****


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.55
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.38
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.47
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907967
  j =  2                              :            46009
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908593
  j =  2                              :            45696
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.71e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.33e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17272.56
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.19
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.00
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.82
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.37
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.53
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.91
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4731.00
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.25
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.89
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.80e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.79
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.49
p-value of test                       :    0.9928

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.57
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999956672

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.63
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999838433

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:08.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 18  BirthdaySpacings, t = 8        1 -  8.3e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61964301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.47
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.35
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908400
  j =  2                              :            45794
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907880
  j =  2                              :            46054
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.00
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.68
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.73
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.26
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.15
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.57
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.94
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.89
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.40
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.33
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.87
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:26.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.11
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.56
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999863840

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.64
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000069781

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:46.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62980109.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  505.69
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.36
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7169.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.22
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4871.44
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:55.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908126
  j =  2                              :            45931
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908271
  j =  2                              :            45860
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.92e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.87
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.95
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.58
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.27
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.40
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.60
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.19
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.90
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.09
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.80
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.87
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.33
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.61
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9764.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:33.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4680.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12022.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999991619

Normal statistic for number of bits   :  -0.066
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.38
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999993368

Normal statistic for number of bits   :  -0.052
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.046
p-value of test                       :    0.48

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:54.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42991630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     841
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9950

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.75
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.96
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:51.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907876
  j =  2                              :            46062
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908361
  j =  2                              :            45815
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.9903

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.01e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:27.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.67
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.53
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.32
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.14
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.56
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:31.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.68
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.57
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.00
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.70
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000032047

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.78
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000095014

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:51.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44335133.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.69
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.53
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.25
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.40
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:52.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908409
  j =  2                              :            45791
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45574
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869574
  j =  1                              :        399908855
  j =  2                              :            45568
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:27.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.12
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.49
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.07
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.25
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.02
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.61
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.16
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.03
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5196.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.62
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.88
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.27
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.24
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.92
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.80
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999956438

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.28
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000010972

Normal statistic for number of bits   :   0.087
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:09.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44957725.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5511
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.09
p-value of test                       :  8.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    4.35
p-value of test                       :  5.9e-3

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     117
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  367.56
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.04
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.99
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.19
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907895
  j =  2                              :            46048
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45954
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869954
  j =  1                              :        399908094
  j =  2                              :            45950
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.66
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.72
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.12
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.07
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.16
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.60
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.47
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.27
p-value of test                       :  7.1e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.14
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.32
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.36
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.29e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4619.48
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3917.05
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.39
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999916640

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.86
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000028930

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:43.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46137373.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4190
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.96
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.11
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.18
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.47
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:49.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908244
  j =  2                              :            45875
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45681
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869681
  j =  1                              :        399908644
  j =  2                              :            45669
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.56
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.96
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   14.86
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.88
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.47
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.86
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.26
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.60
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.08
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.06
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.41
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.10
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.67
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.40
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.49
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10292.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.43
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000056821

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.28
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000096217

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.67
p-value of test                       :    0.9962

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.19
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:20.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46891037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1327.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.30
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:52.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908376
  j =  2                              :            45803
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908285
  j =  2                              :            45853
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17187.13
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.92
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.46
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.51
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.13
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.83
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.12
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.85
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.83
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.41
p-value of test                       :    0.9921

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.67e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.27
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999972593

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.54
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999995546

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:25.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47939613.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    3.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.38
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.88
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908077
  j =  2                              :            45957
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908168
  j =  2                              :            45910
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.85
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17908.38
p-value of test                       :  5.5e-3



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.96
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.22
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.41
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.45
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.36
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.11
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.52
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.79
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.25
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.49
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.56
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000130897

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   28.56
p-value of test                       :    0.9983


-----------------------------------------------
Total number of bits:  7999962126

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    2.50
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:25.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48955421.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.38
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45986
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869986
  j =  1                              :        399908031
  j =  2                              :            45980
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908247
  j =  2                              :            45869
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.68
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.31
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.61
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.27
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  259.49
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.03
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.38
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.23
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:34.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.12
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999879770

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.87
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999924314

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.06

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:48.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50003997.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    6.55
p-value of test                       :  5.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.93
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.21
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.71
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.57
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46207
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870207
  j =  1                              :        399907590
  j =  2                              :            46199
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45396
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869396
  j =  1                              :        399909210
  j =  2                              :            45392
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.76e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.03
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17658.26
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.76
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.69
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.79
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.74
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.75
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.42
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.26
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5168.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.76
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.39
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.46
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10276.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.71
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.75
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999944000

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.55
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000074710

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:05.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         5.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51052573.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.23
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.05
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908074
  j =  2                              :            45957
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908857
  j =  2                              :            45570
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.07
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.03
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.79
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.52
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.05
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.62
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.68
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.37
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.68
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.69
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.07
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9636.78
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.60
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000102223

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.75
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999932360

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    2.60
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:34.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52101149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:37.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9904

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.92
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.73
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908580
  j =  2                              :            45701
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908618
  j =  2                              :            45682
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.08
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.59
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.20
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.72
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.50
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.44
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.73
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.37
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.97
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  1.9e-4    *****

Anderson-Darling statistic = A2       :    9.33
p-value of test                       :  3.1e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10605.71
p-value of test                       :  1.3e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11508.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.24
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999894692

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.78
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999864266

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:38.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 90  HammingWeight2, r = 0           1.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53182493.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5535
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    4.31
p-value of test                       :  6.2e-3

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.39
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.70
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.78
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908258
  j =  2                              :            45871
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45577
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869577
  j =  1                              :        399908849
  j =  2                              :            45571
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.22
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.80
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.14
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.69
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.26
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.41
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.56
p-value of test                       :  5.2e-3

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.01e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.76
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.00
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.81
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.55
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000138913

Normal statistic for number of bits   :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.74
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999877298

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:48.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54231069.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:26.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.43
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4925.95
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45415
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869415
  j =  1                              :        399909172
  j =  2                              :            45411
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908092
  j =  2                              :            45945
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.47
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.05
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.90
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.87
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.70
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.16
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.47
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999952514

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.57
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000047638

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:56.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55246877.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.28
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.40
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908204
  j =  2                              :            45895
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908481
  j =  2                              :            45752
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:30.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-3
p-value of test                       :    0.9990

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  175.33
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.96
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.09
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.47
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.27
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.90
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.91
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.84
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 2.33e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.05
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.66
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10216.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.32
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000085150

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.93
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000047257

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:30.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56295453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:10.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.29
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.75
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6882.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:20.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.29
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9935


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907786
  j =  2                              :            46104
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908466
  j =  2                              :            45764
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.61e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:12.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:30.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.18
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.45
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.31
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.74
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.62
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.77
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.46
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.10
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.03
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10223.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.03
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.41
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000013351

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.87
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999816830

Normal statistic for number of bits   :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:56.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57344029.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5500
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:38.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.24
p-value of test                       :  2.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.05
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.48
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5239.76
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:53.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908208
  j =  2                              :            45893
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908829
  j =  2                              :            45581
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17835.08
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.43
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.46
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.12
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.97
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.39
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.60
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.86
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.29
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.25
p-value of test                       :    0.9962

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9695.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:03:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.74
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999950999

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.27
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000062851

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:56.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58359837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5270
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.68
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45492
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869492
  j =  1                              :        399909019
  j =  2                              :            45486
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908533
  j =  2                              :            45732
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.90e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -4.54e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.084
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.60
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.75
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.17
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.44
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.22
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.49
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.11
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.52
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.94
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.12
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.64
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.07
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.98
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4666.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.16
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000045928

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.39
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999898151

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:24.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59408413.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1242
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334362
  j =  1                              :        599997516
  j =  2                              :             1242
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.09
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:37.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.17
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.19
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  291.87
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.69
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.68
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907922
  j =  2                              :            46036
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907805
  j =  2                              :            46093
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.88e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:29.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:28.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.50
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17678.21
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.01
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.16
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.45
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.97
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4788.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  148.93
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.08
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.65
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.34
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4314.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.58
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999907907

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.87
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999840287

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:39.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60489757.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    4.14
p-value of test                       :  7.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.47
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   38.67
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.39
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.05
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908088
  j =  2                              :            45953
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908075
  j =  2                              :            45961
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:30.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.44
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.13
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17593.82
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.08
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.99
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.92
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.88
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.35
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.40
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5073.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12118.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.72
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999996176

Normal statistic for number of bits   :  -0.030
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.60
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999981383

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:14.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 94  HammingCorr, L = 1200           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61571101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908330
  j =  2                              :            45823
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907661
  j =  2                              :            46165
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.21
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.95
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.62
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.97
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.20
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.30
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.72
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.62
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.54
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -403.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.66e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.48
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.90
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000018898

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.19
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999996851

Normal statistic for number of bits   :  -0.025
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.99

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:35.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62619677.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.15
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   36.55
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.61
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.82
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45486
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869486
  j =  1                              :        399909030
  j =  2                              :            45482
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907942
  j =  2                              :            46017
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.08e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.28
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.59
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17267.70
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.27
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.57
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.67
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.75
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.74
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.97
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.59
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.63
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -401.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.16
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.62
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    6.70
p-value of test                       :  5.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5216.45
p-value of test                       :  6.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.76
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.02
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999923642

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.81
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000099568

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:51.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 96  HammingIndep, L=30, r=27        6.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43024399.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.41
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5141.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46213
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870213
  j =  1                              :        399907576
  j =  2                              :            46209
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908440
  j =  2                              :            45780
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.52e-5
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.33
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.35
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.65
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.52
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.03
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.76
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.09
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.07e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.51
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   42.00
p-value of test                       :  1.1e-3



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.35
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.50e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.22
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000094108

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.07
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999962285

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    5.19
p-value of test                       :  2.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.76
p-value of test                       :    0.9971

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:08.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43778058.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:38.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.57
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.58
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908813
  j =  2                              :            45589
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908203
  j =  2                              :            45897
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17126.46
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.35
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.49
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.04
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.30
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.90
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.31
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.34
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.59
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.48
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.41
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.55
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.08
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999867083

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.45
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000035641

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:22.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44793866.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.74
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.51
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908312
  j =  2                              :            45841
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908510
  j =  2                              :            45739
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.72e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17651.80
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   46.11
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.65
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.70
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.27
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.10
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.26
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.16
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.47
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -403.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.13e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.68
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.06
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.11
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000022081

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.94
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000014575

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:35.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45809674.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    4.13
p-value of test                       :  7.5e-3

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1333.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4783.06
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46214
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870214
  j =  1                              :        399907579
  j =  2                              :            46200
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908055
  j =  2                              :            45962
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.069
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.61
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.56
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.86
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.48
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.97
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  467.11
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.28
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.97
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.94
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:58.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:32.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.71
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000178312

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.04
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999952661

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:50.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46759946.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5239
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7577
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     257
p-value of test                       :    0.9939

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:36.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.58
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.06
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908383
  j =  2                              :            45804
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45550
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869550
  j =  1                              :        399908903
  j =  2                              :            45544
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.44e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.64
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.25
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.82
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.03
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.71
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.38
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.97
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.86
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.79
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.78
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.30
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.88
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.35
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.50
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4710.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11459.35
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.12
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999842585

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.68
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000114199

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.34

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:38.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47841290.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    4.01
p-value of test                       :  8.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    3.62
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.11
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9911

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.16
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908488
  j =  2                              :            45747
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908283
  j =  2                              :            45854
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.64
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.22
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.83
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.61
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.78
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.36
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.36
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.46
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.49
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.64
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.11
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.70
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.99
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000182149

Normal statistic for number of bits   :    1.44
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000057886

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:58.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48889866.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.70
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.43
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1327.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6795.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.94
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907978
  j =  2                              :            46011
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908519
  j =  2                              :            45733
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.83
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.43
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.97
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.87
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.01
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.47
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5178.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  266.76
p-value of test                       :  1.1e-3


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.41
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.65
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.68
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -401.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.39
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 3.81e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.43
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:34.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12238.31
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.47
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000064822

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.84
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999840266

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:31.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49971210.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.38
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7174.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.11
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.67
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:01.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908182
  j =  2                              :            45906
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45616
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869616
  j =  1                              :        399908772
  j =  2                              :            45608
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.26
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.80
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.33
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.56
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.87
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.53
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.31
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.56
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.75
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.30
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.96
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.016
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12152.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.76
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999990059

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.38
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000042850

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.024
p-value of test                       :    0.49

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:11.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51019786.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:38.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.35
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7207.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:33.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.61
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.06
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.69
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46215
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870215
  j =  1                              :        399907572
  j =  2                              :            46211
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908488
  j =  2                              :            45750
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17270.48
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.33
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.35
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.01
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.07
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.48
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.79
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.84
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.81
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.51
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:33.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.25
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.53
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999983489

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.24
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999977471

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.62
p-value of test                       :  4.4e-3

Sample variance                       :    2.44
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:56.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52035594.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4495
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.91
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.28
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.18
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.83
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.77
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46266
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870266
  j =  1                              :        399907471
  j =  2                              :            46260
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908083
  j =  2                              :            45951
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17511.80
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.57
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.63
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.69
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.80
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.78
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.61
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.58
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.52
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.22
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.44
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.45
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.35
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.51
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4341.11
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.91
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999892280

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.26
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999882047

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    6.26
p-value of test                       :  8.0e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.29
p-value of test                       :  5.0e-4    *****

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:40.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 103  AutoCor, d=1, r=0               5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53116930.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:37.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.80
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907828
  j =  2                              :            46080
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907997
  j =  2                              :            45997
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17549.89
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.32
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.52
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.60
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.18
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  582.93
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.98
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.38
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.68
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.06
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.89
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.68
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:28.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12180.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.16
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999942071

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.29
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000010465

Normal statistic for number of bits   :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.22
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:55.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54165506.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.09
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9955


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.56
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.32
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908468
  j =  2                              :            45763
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907993
  j =  2                              :            45999
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.45e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   75.53
p-value of test                       :  1.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.49
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.00
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.70
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.60
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.88
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.18
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.35
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.38
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.59
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.29
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5027.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.46
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.47
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999955415

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.31
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999936401

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:19.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 63  WeightDistrib, r = 10           1.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55214082.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.75
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   39.33
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:20.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.48
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.03
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907950
  j =  2                              :            46019
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907740
  j =  2                              :            46127
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:12.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:29.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17217.97
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.78
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.94
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.88
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.76
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.28
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.80
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.27
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.79
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5163.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.11
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.79
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    2.50
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.24
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:24.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5084.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12060.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.45
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000055849

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.48
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999891986

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:17.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56262658.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    3.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.12
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9909

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6930.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.78
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5241.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908347
  j =  2                              :            45816
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908801
  j =  2                              :            45595
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 3.32e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:18.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:28.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:29.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:29.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17112.89
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.79
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.12
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.92
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.96
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -401.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.00e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:25.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.47
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.25
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999906602

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.48
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000095404

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:07.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57278466.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.73
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.11
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.43
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46187
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870187
  j =  1                              :        399907632
  j =  2                              :            46175
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908728
  j =  2                              :            45630
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.16e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17284.09
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.61
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.72
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.94
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.37
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.48
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.67
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.38
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.16
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.90
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10343.37
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5186.90
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3971.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.92
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000028648

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.39
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000067267

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:04.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58327042.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:36.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7331.63
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.49
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45527
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869527
  j =  1                              :        399908952
  j =  2                              :            45515
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908278
  j =  2                              :            45858
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:29.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.94
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:28.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.94
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.75
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.82
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.83
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.30
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.78
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.47
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10283.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.49
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000041953

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.41
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999994364

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:15.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59375618.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6997.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.22
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908049
  j =  2                              :            45971
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908317
  j =  2                              :            45837
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.36
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.79
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.43
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4811.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.12
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.30
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.75
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.51
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:45.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4754.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.48
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000060058

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.23
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999893417

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:13.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60424194.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5588
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:29.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.86
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.54
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908184
  j =  2                              :            45902
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907991
  j =  2                              :            45997
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.20
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.36
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.67
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4773.84
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.10
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.93
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.83
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.07
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.84
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:03:40.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.40
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5116.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999997283

Normal statistic for number of bits   :  -0.021
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.84
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999868169

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:48.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61472770.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.00
p-value of test                       :  9.2e-3

Test on the Nm values of W_{n,i}(mNP1):    7.99
p-value of test                       :  1.2e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     254
p-value of test                       :    0.9964

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:46.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.10
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1545.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:29.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.74
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.54
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908427
  j =  2                              :            45785
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908187
  j =  2                              :            45899
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17660.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.74
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.68
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.56
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.04
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.01
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.42
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.53
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.12
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.03
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.50
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4317.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.91
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999897908

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.79
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000135133

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.55
p-value of test                       :    0.9947

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.035
p-value of test                       :    0.51

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:02.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           7.2e-4
 24  ClosePairs mNP1, t = 9          1.2e-4
 74  RandomWalk1 R (L=50, r=0)       0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62521346.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9926


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     655
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.48
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.28
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.25
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.36
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:53.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45632
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869632
  j =  1                              :        399908743
  j =  2                              :            45618
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908049
  j =  2                              :            45968
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.45e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:27.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:28.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17705.40
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.85
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.72
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.55
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.46
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.17
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.80
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.55
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.27
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.26
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.07
p-value of test                       :    0.02

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.97
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000043885

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.35
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999978683

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:25.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43057168.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.01
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.87
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.59
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908530
  j =  2                              :            45726
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908099
  j =  2                              :            45949
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.73e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:29.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17318.46
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.00
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.14
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.27
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.73
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.28
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.56
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.89
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.83
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.74
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.39
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.28
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.50
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999952463

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.54
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999891344

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    5.49
p-value of test                       :  1.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.14
p-value of test                       :  8.4e-4    *****

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:35.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 104  AutoCor, d=3, r=0               8.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44072976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7118.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5272.39
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:00.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908314
  j =  2                              :            45840
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908116
  j =  2                              :            45933
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17564.27
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.52
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.78
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.30
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.42
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.82
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.14
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.45
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.87e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.67
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.61
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4329.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.57
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999910046

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.05
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  8000117922

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:25.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45252624.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.16
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.92
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5221.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908456
  j =  2                              :            45769
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907940
  j =  2                              :            46024
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.23e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:27.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.58
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.97
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.67
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.94
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.28
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.21
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.40
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.90
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.77
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.80
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.37
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.29
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999948062

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.92
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000131797

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:47.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46333968.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    4.14
p-value of test                       :  7.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.89
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.48
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:30.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.78
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908651
  j =  2                              :            45673
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46292
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870292
  j =  1                              :        399907421
  j =  2                              :            46282
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.07e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.30e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.63
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.55
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.17
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.58
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.62
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4733.30
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.92
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4656.72
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.69
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999957971

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.54
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000007201

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.02

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:00.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47448076.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4189
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.94
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.55
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907979
  j =  2                              :            46006
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908115
  j =  2                              :            45938
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17863.25
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.71
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.94
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4760.93
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.48
p-value of test                       :    0.9911


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.44
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.78
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.31
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.22
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000000556

Normal statistic for number of bits   : 4.40e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.62
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999936680

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:59.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48431116.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9936

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6815.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:28.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.45
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.98
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908633
  j =  2                              :            45679
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908196
  j =  2                              :            45899
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.47e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.79
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.00
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.53
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.99
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.18
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.25
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.72
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.52
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.73
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.20
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    4.90
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5203.36
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.48
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999891893

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.47
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000024715

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.22
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:25.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 95  HammingIndep, L=30, r=0         9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49446924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.69
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.98
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:30.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.22
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908192
  j =  2                              :            45898
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908271
  j =  2                              :            45863
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 4.08e-4
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    6.41
p-value of test                       :  6.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.02
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.93
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.74
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.68
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.13
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.62
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.14
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.74
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.31
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.82
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.48
p-value of test                       :  5.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.05
p-value of test                       :  1.1e-3

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.91e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  8.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.60
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9765.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.07
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999992702

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.05
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000096262

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:04.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              6.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 85  Fourier3, r = 27               1 -  8.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50397196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:27.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   17.32
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.86
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4898.11
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46299
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870299
  j =  1                              :        399907407
  j =  2                              :            46289
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908357
  j =  2                              :            45820
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:09.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.16e-5
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.89
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17245.16
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.58
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.45
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.22
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.21
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.27
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.01
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.41
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3935.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.43
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999852026

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.44
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999973160

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:24.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51609612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.07
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.44
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.23
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908885
  j =  2                              :            45553
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908149
  j =  2                              :            45921
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.89e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.77
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.83
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.49
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.38
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.29
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.46
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.56
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.54
p-value of test                       :    0.9980


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.68
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.41
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.84
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.52
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000024856

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.51
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000144811

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:57.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52625420.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7546
p-value of test                       :  4.1e-3


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:30.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.47
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.39
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908324
  j =  2                              :            45838
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908116
  j =  2                              :            45936
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.72e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17684.28
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.75
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.12
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.22
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.50
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.56
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.51
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.26
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.90
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.9903

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10357.94
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.62
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999923345

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000008635

Normal statistic for number of bits   :   0.068
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:23.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53673996.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    5.98
p-value of test                       :  1.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     824
p-value of test                       :    0.9946

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.16
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.68
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908826
  j =  2                              :            45578
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908594
  j =  2                              :            45700
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.52e-5
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.38
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.77
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.48
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.13
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.94
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.46
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.56
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.27
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.26
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.22
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.16
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.68
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4337.44
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.97
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999919661

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.51
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000063292

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.21
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:52.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54722572.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.37
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1326.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:30.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908273
  j =  2                              :            45862
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908378
  j =  2                              :            45808
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.67e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.36
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.78
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.97
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.51
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.23
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.41
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.77
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.98
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5176.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.42
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.59
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.01
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.66
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.06
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.13
p-value of test                       :    0.9947


-----------------------------------------------
Total number of bits:  7999906494

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.12
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000204400

Normal statistic for number of bits   :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         : -9.48e-3
p-value of test                       :    0.50

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:03.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55836684.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.11
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.29
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.72
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:31.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.72
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.20
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:52.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45438
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869438
  j =  1                              :        399909126
  j =  2                              :            45434
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908161
  j =  2                              :            45915
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  7.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17233.63
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.52
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.30
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.70
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.99
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.71
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.58
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.31
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.72
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.35
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.31
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.58
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.42
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.63
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.23
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.06
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.46
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.08
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5036.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.11
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999991721

Normal statistic for number of bits   :  -0.065
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.55
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000087118

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:14.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56754188.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5590
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     655
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.33
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.99
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.30
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5201.26
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:55.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908074
  j =  2                              :            45954
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45780
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869780
  j =  1                              :        399908443
  j =  2                              :            45774
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17744.55
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.49
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  608.31
p-value of test                       :  6.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.51
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.74
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.18
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5250.99
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.06
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.43
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5156.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.62
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.98
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.53
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.09
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.42
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999980003

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.54
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999932564

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:40.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 J (L=1000, r=0)     6.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57737228.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.13
p-value of test                       :    0.9994    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.64
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.56
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908112
  j =  2                              :            45941
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908466
  j =  2                              :            45761
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9903


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.46
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.92
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.44
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.84
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.51
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.09
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.99
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.06
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.73
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.31
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.35
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10283.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.77
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000010918

Normal statistic for number of bits   :   0.086
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.72
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000063682

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:39.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58720268.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    4.92
p-value of test                       :  3.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.97
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.34
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.92
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.91
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:51.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907717
  j =  2                              :            46137
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907614
  j =  2                              :            46187
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9978


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.89e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17171.34
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.31
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.22
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.19
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.19
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.32
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.47
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.50
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.11
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.11
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.19
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.38e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.98
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.16
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10197.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.10
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000050509

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.71
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000089650

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:11.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59834380.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    7.32
p-value of test                       :  2.5e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9936

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.61
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908077
  j =  2                              :            45957
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46503
p-value of test                       :  1.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870503
  j =  1                              :        399907003
  j =  2                              :            46485
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.56e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.46
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.71
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.63
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.37
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.97
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.03
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.67
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.21
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.38
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.82
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.55
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000061123

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.59
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000034579

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:18.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP, t = 5           2.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60948492.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1495
p-value of test                       :  2.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334615
  j =  1                              :        599997010
  j =  2                              :             1495
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.14
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1512.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.96
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5252.66
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45327
p-value of test                       :    0.9951


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869327
  j =  1                              :        399909352
  j =  2                              :            45315
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908861
  j =  2                              :            45562
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.77
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.64
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.63
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.95
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.79
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.75
p-value of test                       :  5.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.71
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.08
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.00
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.65
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11569.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.02
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999945947

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.07
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000005314

Normal statistic for number of bits   :   0.042
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:18.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           2.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62062604.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.78
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.31
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.77
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.98
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.86
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.67
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:48.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908573
  j =  2                              :            45712
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907777
  j =  2                              :            46110
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.10e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.05
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.16
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.45
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.47
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.17
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.55
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.07
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.50
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.52
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.71
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.01
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.62
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000128587

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000096367

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:38.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63111180.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:47.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.22
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.96
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.02
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4812.23
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:53.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45597
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869597
  j =  1                              :        399908811
  j =  2                              :            45587
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908008
  j =  2                              :            45996
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.04e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17315.79
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.74
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.29
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.24
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.88
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.65
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.31
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.64
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.29
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  462.95
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.05
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.03
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.53
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.38
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.74
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.33
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:31.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999966746

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.07
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999895391

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:35.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43089937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5311
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.73
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1337.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.90
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.06
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907859
  j =  2                              :            46066
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45509
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869509
  j =  1                              :        399908989
  j =  2                              :            45495
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  5.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.86
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.99
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.15
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.02
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.50
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.67
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.00
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3907.29
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.45
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000105784

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.43
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999950801

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:14.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43646993.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.16
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6861.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.70
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:53.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907705
  j =  2                              :            46146
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907892
  j =  2                              :            46051
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:29.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.91
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.87
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.60
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.71
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.25
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.65
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.49
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.78
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.46
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.76
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.14
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.70
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.70e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9696.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10326.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.62
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000120511

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.22
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000070957

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.099
p-value of test                       :    0.46

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:56.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45121553.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4164
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9977

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.95
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:58.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908615
  j =  2                              :            45691
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907718
  j =  2                              :            46138
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.42e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.41
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.93
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.02
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.82
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.64
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.06
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.65
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.01
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.30
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.55
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.64
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.58
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.73
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.50
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.52
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000101371

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.61
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999997175

Normal statistic for number of bits   :  -0.022
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:08.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46006299.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4491
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7129
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7046
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.66
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.42
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.74
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908435
  j =  2                              :            45775
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908050
  j =  2                              :            45969
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.81
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.49
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.97
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   91.52
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.57
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.35
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.25
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.67
p-value of test                       :    0.9925


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.95
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:32.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.08
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000196330

Normal statistic for number of bits   :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.61
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000007483

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:08.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47382555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.08
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:31.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.95
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.20
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908192
  j =  2                              :            45895
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908325
  j =  2                              :            45836
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.47e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17165.90
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.17
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.48
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.37
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.53
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.77
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.49
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.42
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.55
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.34
p-value of test                       :    0.9927


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.77
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11946.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.32
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000061561

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.18
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999846218

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:10.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48201755.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.56
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:39.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.25
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:55.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908434
  j =  2                              :            45777
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908393
  j =  2                              :            45793
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17572.11
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.34
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.34
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.99
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.69
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.76
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.24
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  277.08
p-value of test                       :  2.5e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.95
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.11
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.73
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.51
p-value of test                       :    0.9926

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.71
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4787.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.26
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.76
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000094774

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.24
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000148243

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:50.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    2.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49283099.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9946


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.46
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.76
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4876.82
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908008
  j =  2                              :            45990
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908044
  j =  2                              :            45969
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.87
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.48
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.85
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.13
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.18
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.19
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.85
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.61
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.06
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000024001

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.77
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000111754

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:27.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50331675.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    3.09
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.58
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.02
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:48.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907613
  j =  2                              :            46189
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45622
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869622
  j =  1                              :        399908759
  j =  2                              :            45616
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.63
p-value of test                       :  1.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.31
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.43
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.21
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.88
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.94
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.07
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.98
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.94
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.92
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.84
p-value of test                       :    0.9966


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.79
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 3.45e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    6.99
p-value of test                       :  3.7e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  136.15
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.09
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.59
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.45
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000023593

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.36
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999923654

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:28.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 58  AppearanceSpacings, r = 27      1.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 88  PeriodsInStrings, r = 0         0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51314715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997109
  j =  2                              :             1444
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:34.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.07
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:56.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908627
  j =  2                              :            45682
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.66e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.36
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.08
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.30
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.24
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.57
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.29
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.59
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.76
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.57
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.43
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.88
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.04
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999899012

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.15
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999940091

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:51.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52199451.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    5.03
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.50
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.79
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908469
  j =  2                              :            45761
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46306
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870306
  j =  1                              :        399907391
  j =  2                              :            46300
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.84e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.92
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.52
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.55
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.58
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.49
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.06
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.87
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.99
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.75
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.12
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.65
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.50
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.76
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.86
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3863.18
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.14
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000002491

Normal statistic for number of bits   :   0.020
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.90
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000142096

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:02.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53248027.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4175
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    3.97
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6887.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.64
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.47
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.62
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908299
  j =  2                              :            45840
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908147
  j =  2                              :            45922
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   52.53
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.17
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.65
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.45
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.42
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.52
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.18
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.90
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.68
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.25
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.33
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9660.53
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.79
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000040240

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.68
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000029740

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:51.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54296603.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.49
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.71
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.43
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908615
  j =  2                              :            45691
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907790
  j =  2                              :            46099
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    5.19
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.43
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.47
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.10
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.62
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.35
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.97
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.63
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.64
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -401.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.33
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.68
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.75
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.22
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.89
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000093844

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.65
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000025180

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    3.12
p-value of test                       :  9.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55312411.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    3.98
p-value of test                       :  8.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     830
p-value of test                       :    0.9904

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9965

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.94
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:29.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.50
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.47
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45447
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869447
  j =  1                              :        399909111
  j =  2                              :            45437
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908777
  j =  2                              :            45607
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.76e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17335.40
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.82
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.91
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.29
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.86
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.69
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  305.15
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.90
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.16
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.02
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.86
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.13
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.35
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999908738

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.68
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000060478

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:13.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56360987.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9925

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.04
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:03.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908148
  j =  2                              :            45923
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908474
  j =  2                              :            45760
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.57
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.46
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.58
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.87
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.66
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.98
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.67
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.06
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.04
p-value of test                       :  6.7e-3


-----------------------------------------------
Total number of bits:  8000075550

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.78
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000040906

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57409563.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:36.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    3.37
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     256
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.36
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.39
p-value of test                       :  9.2e-3


-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.16
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908645
  j =  2                              :            45676
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908074
  j =  2                              :            45960
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.07e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:12.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:30.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17689.93
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.57
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.79
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.07
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.36
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.93
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9700.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 6.16e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.63
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000103456

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.50
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999940916

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:57.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58458139.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.93
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    4.00
p-value of test                       :  8.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.65
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.18
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45986
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869986
  j =  1                              :        399908030
  j =  2                              :            45982
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46069
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870069
  j =  1                              :        399907865
  j =  2                              :            46063
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:29.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.53
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.65
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.33
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.39
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.13
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.48
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.37
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.74
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.43
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -401.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.91
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.83
p-value of test                       :    0.9953


-----------------------------------------------
Total number of bits:  7999917987

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.55
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999893672

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:11.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59506715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5249
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4185
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     823
p-value of test                       :    0.9951

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    3.38
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7320.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:29.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.95
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:57.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908100
  j =  2                              :            45947
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908754
  j =  2                              :            45620
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.77e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.40e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:29.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:29.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:29.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:29.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.14e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.80
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.04
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.59
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.34
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.50
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.59
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.61
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.48
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.97
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.74
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4688.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.71
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.49
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000008590

Normal statistic for number of bits   :   0.068
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.81
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999978080

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.18
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.53
p-value of test                       :  5.7e-3

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:07.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60555291.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.98
p-value of test                       :  9.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.06
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4857.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:56.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908187
  j =  2                              :            45899
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908456
  j =  2                              :            45766
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  7.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:19.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.04
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17158.84
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.58
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   99.79
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.63
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.78
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.80
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.07
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.53
p-value of test                       :  4.6e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.06
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.61
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10294.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.22
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999975098

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000147562

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:29.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61603867.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.72
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908588
  j =  2                              :            45700
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908142
  j =  2                              :            45923
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9915


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:18.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:12.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.83
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:28.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.9937

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17138.36
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.00
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.43
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.45
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.32
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.10
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.92
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.69
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.42
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.31
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:09.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10212.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.78
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000140794

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.75
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000053773

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:47.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62652443.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.10
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.71
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.75
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908078
  j =  2                              :            45955
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45514
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869514
  j =  1                              :        399908980
  j =  2                              :            45498
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.76e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.07
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:28.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17484.33
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.15
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.84
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.35
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.78
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.12
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.39
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.63
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.27
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12102.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.13
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999850922

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.60
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999943589

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:22.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43122706.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4491
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.42
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.47
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:54.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908665
  j =  2                              :            45663
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908558
  j =  2                              :            45715
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 5.83e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.26
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.81
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.44
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.79
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.23
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.91
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.42
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.10
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.52
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.18
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000105253

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.48
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999974165

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:06.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44040210.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    3.74
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.36
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.48
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.37
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:58.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908353
  j =  2                              :            45816
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908045
  j =  2                              :            45973
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.88e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.99
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:30.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   88.25
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17637.68
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.41
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.54
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.02
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.30
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.74
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.20
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.13
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.25
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.52
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.84
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000074905

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.93
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000156043

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:30.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44924946.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7237.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:29.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.65
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.47
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5216.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908068
  j =  2                              :            45960
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908146
  j =  2                              :            45924
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:27.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.50
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.93
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.07
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.40
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.17
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.96
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.52
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.90
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:32.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4262.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12143.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.36
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999877028

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.27
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000111631

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:26.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46170130.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5540
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.72
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.76
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.18
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.01
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907948
  j =  2                              :            46020
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908840
  j =  2                              :            45574
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.29e-5
p-value of test                       : 1 -  4.3e-5    *****

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.38
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.27
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.39
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.80
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.91
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.93
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.71
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.75
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.81
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.47
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.80
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.14
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    6.69
p-value of test                       :  5.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9533.75
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.79
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999986702

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.88
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999976910

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:29.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 91  HammingWeight2, r = 27          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47185938.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.68
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.09
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908478
  j =  2                              :            45755
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908578
  j =  2                              :            45702
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.87
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.06
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.00
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.86
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.65
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.51
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.31
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -403.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9642.53
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.84
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4642.45
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.81
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.42
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999881567

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.91
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999962345

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:05.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48103442.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9975

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:30.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.95
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.61
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908383
  j =  2                              :            45804
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907930
  j =  2                              :            46029
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.96e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:27.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.26
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.50
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.22
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.69
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.46
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.48
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.27
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.48
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.96
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.21
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.52
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.55
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.95
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:38.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.85
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000083833

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.56
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999990164

Normal statistic for number of bits   :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    0.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:55.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49152018.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    3.64
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:37.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.85
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.50
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.92
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46169
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870169
  j =  1                              :        399907670
  j =  2                              :            46153
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908892
  j =  2                              :            45551
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.54
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:27.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   75.11
p-value of test                       :  2.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.55
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.56
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.73
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.36
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.54
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.28
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.77
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   32.34
p-value of test                       :  1.2e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.56e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9730.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4657.87
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.52
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999889967

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.08
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000153700

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:51.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           2.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50495506.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.31
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.87
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908526
  j =  2                              :            45734
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908195
  j =  2                              :            45895
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17813.54
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.22
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.84
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.72
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.41
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.30
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.89
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.36
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.75
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.28
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.42
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  464.64
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.73
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.70
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.36
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999935882

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000088015

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:07.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51642386.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7054
p-value of test                       :    0.9990    *****


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:18.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.41
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1271.77
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.41
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:03.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908426
  j =  2                              :            45778
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908163
  j =  2                              :            45908
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.27e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.31e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.11
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.47
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.45
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.45
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.57
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4273.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.84
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000155290

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.47
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999990362

Normal statistic for number of bits   :  -0.076
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:39.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 19  BirthdaySpacings, t = 8         0.9990 
 36  Gap, r = 0                      0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52592658.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.54
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1311.94
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:31.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.27
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.93
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:00.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45457
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869457
  j =  1                              :        399909088
  j =  2                              :            45453
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908372
  j =  2                              :            45811
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.48
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.52
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.60
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.39
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.52
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.20
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.40
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.35
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.32
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.76
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:34.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5068.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4313.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11498.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.45
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000024673

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.81
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000029779

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:55.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53608466.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.66
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   12.59
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:29.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.75
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908681
  j =  2                              :            45649
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45468
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869468
  j =  1                              :        399909069
  j =  2                              :            45458
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.48
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.60
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17492.84
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.16
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.68
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.23
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.63
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.18
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.19
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.94
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3904.21
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12122.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.55
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000001861

Normal statistic for number of bits   :   0.015
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.92
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999972038

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:16.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54624274.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.60
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.14
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.16
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.88
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908037
  j =  2                              :            45977
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907847
  j =  2                              :            46072
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-6
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    : 3.10e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.35e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17506.02
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.64
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.98
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.78
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.11
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.32
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.35
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.00
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.90
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.77
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.98
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.77
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.59
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.78
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.64
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.82
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000033976

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.92
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000045838

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:13.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55574546.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7074
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.61
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.31
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:30.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.84
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908709
  j =  2                              :            45638
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908597
  j =  2                              :            45697
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.81
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.44
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17391.71
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.41
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.62
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.55
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.04
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.21
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.50
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.96
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.47
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3930.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12054.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.13
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000010240

Normal statistic for number of bits   :   0.081
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.00
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000069403

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:31.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56557586.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.10
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4892.15
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908033
  j =  2                              :            45979
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908233
  j =  2                              :            45879
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.15e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   14.53
p-value of test                       :  7.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.49
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.13
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.45
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.97
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.32
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.68
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.71
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.70
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9683.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.60
p-value of test                       :  6.0e-3


-----------------------------------------------
Total number of bits:  8000050812

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.60
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999943430

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         : 6.00e-3
p-value of test                       :    0.50

Sample variance                       :    0.18
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:04.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 70  MatrixRank, L=5000              7.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57671698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    3.61
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.03
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.87
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.66
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908421
  j =  2                              :            45785
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908672
  j =  2                              :            45655
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:27.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:27.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.77
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17370.90
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.50
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.06
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.84
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.42
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.71
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.89
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.81
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.09
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.39e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.46
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.99
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11531.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.71
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999971408

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.76
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999831428

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:16.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58753042.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    3.41
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.46
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6703.76
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:27.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  154.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.35
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:23.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908384
  j =  2                              :            45808
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907773
  j =  2                              :            46112
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.25e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  103.68
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.99
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17654.42
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.07
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.73
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.20
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  438.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.74
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.37
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.38
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.38
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.23
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -3.13
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12150.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.56
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000022786

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.97
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999909557

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:47.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 93  HammingCorr, L = 300            0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59801618.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    3.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:29.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.33
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.92
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.27
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908578
  j =  2                              :            45711
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907923
  j =  2                              :            46031
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.83e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -9.71e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.50
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.53
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.32
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.67
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.79
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.27
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.62
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.11
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.15
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.77
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.82
p-value of test                       :  5.9e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.51
p-value of test                       :  6.1e-3

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.89
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10383.53
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.095
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.08
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999908948

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000057202

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:22.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60981266.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.44
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.31
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.07
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4886.75
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908293
  j =  2                              :            45849
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908354
  j =  2                              :            45814
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.96e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.45e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.71
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17545.26
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.76
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.16
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.69
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.16
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.57
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.94
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.63
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.11
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999952058

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.68
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999938774

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:14.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61997074.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     347
p-value of test                       :  4.3e-3

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9928

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9944


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   25.16
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.16
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.60
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:01.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908290
  j =  2                              :            45849
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908324
  j =  2                              :            45832
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.41
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17614.82
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.22
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.04
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.45
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.27
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  584.52
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.45
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   99.31
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.39
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  303.48
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.45
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  316.46
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.11
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.96
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.14
p-value of test                       :  6.8e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.53
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:27.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.19
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000056662

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.82
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000047797

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:08.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         0.9997 
 79  RandomWalk1 H (L=10000, r=15)   0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63045660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.46
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    3.06
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.90
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.56
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908513
  j =  2                              :            45739
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907795
  j =  2                              :            46098
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:28.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   91.93
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.57
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.73
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.20
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.08
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.66
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.03
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.16
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.52
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.45
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.77
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.58
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9806.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  2.1e-4    *****

Anderson-Darling statistic = A2       :    6.58
p-value of test                       :  5.7e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5201.74
p-value of test                       :  9.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.94
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.26
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999998423

Normal statistic for number of bits   :  -0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.01
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000019306

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.09
p-value of test                       :  8.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:11.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 96  HammingIndep, L=30, r=27        9.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43155475.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5535
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4204
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  183.82
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.49
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.32
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908266
  j =  2                              :            45864
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45530
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869530
  j =  1                              :        399908942
  j =  2                              :            45526
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.82e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17190.59
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.15
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.96
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.13
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.68
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.66
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.91
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.66
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.94e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.12
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000099487

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.44
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000027955

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:36.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43941907.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5243
p-value of test                       :    0.9923


-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7320.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:29.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.49
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.82
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:53.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46119
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870119
  j =  1                              :        399907767
  j =  2                              :            46109
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908309
  j =  2                              :            45838
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.08
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.32
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.13
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.44
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.78
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.51
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.04
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:59.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:32.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.76
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000098104

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.05
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000011854

Normal statistic for number of bits   :   0.094
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:29.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45154323.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4491
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.12
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.68
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.52
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:56.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908237
  j =  2                              :            45874
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908358
  j =  2                              :            45818
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.06e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.18e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17236.42
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.25
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   64.71
p-value of test                       :  2.3e-5    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.83
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.71
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.34
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.58
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.39
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.36
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.20
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.62
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.99
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10316.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.67
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000085573

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.20
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000029050

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.085
p-value of test                       :    0.53

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:10.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 J (L=50, r=25)      2.3e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45907987.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7091
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9942


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:37.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    4.27
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  100.31
p-value of test                       :  8.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:31.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.77
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.83
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.89
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908427
  j =  2                              :            45782
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.74e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.57
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17122.05
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.42
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.97
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.49
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.19
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.19
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.19
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.79
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4641.61
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.53
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.64
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999975260

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.38
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999856850

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:17.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46858259.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:10.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.38
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.78
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.87
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907775
  j =  2                              :            46108
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907975
  j =  2                              :            46008
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.50e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.05
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.14
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17767.54
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.22
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.82
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.04
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.89
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.25
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.82
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.85
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.19
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.45
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.21
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.59
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.76e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.19
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.05
p-value of test                       :  8.2e-3


-----------------------------------------------
Total number of bits:  7999940886

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.43
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000124270

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:16.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48070675.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.41
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7250.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.77
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.70
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908483
  j =  2                              :            45754
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908697
  j =  2                              :            45650
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.19e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:27.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.11
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.97
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.84
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.56
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.87
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.31
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.46
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9726.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.22
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.82
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999989741

Normal statistic for number of bits   :  -0.081
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   24.31
p-value of test                       :    0.9998    *****


-----------------------------------------------
Total number of bits:  8000001300

Normal statistic for number of bits   :   0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:15.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 102  Run of bits, r = 27             0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49217555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   76.69
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.02
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908629
  j =  2                              :            45681
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908210
  j =  2                              :            45886
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.01e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17269.60
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.04
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.15
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.55
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.26
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.96
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4323.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.54
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999909293

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.09
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999917552

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:08.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 41  Permutation, t = 5              0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50200595.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5255
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    3.72
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9980

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:39.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.41
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907769
  j =  2                              :            46111
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908547
  j =  2                              :            45722
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9983


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.37
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.14
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.64
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.89
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.79
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.40
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.16
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 3.76e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9778.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4673.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5156.29
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.77
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999937922

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.08
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000047821

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:21.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51249156.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    4.29
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.11
p-value of test                       :  7.9e-3

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    4.96
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.45
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.09
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908511
  j =  2                              :            45740
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908596
  j =  2                              :            45699
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17731.07
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.79
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.00
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.29
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.58
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.67
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.62
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.45
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.20
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.19
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.07
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.30
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.87
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5063.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.86
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999951635

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.61
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999984719

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:38.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52330500.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:46.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7514
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:29.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:48.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:49.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.15
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.15
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.16
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.15
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.16
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5218.13
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908278
  j =  2                              :            45855
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907800
  j =  2                              :            46094
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9902


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  9.8e-4    *****

Anderson-Darling statistic = A2       :    5.08
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.64e-4
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.01
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.12
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.76
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.39
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.47
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.94
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.56
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  253.38
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.24
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.33
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.16
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9760.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11640.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11516.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000144349

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.48
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000200146

Normal statistic for number of bits   :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:56:02.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53444612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:52.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   28.32
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.30
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.52
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908433
  j =  2                              :            45776
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45636
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869636
  j =  1                              :        399908731
  j =  2                              :            45630
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:15.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.41e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.20
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.77
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.28
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.22
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.26
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.23
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.96
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.46
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.14
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9794.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9988

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.79
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000105304

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.74
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000107269

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:02.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55115780.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.99
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.57
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.12
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908234
  j =  2                              :            45880
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908115
  j =  2                              :            45935
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:16.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.73
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.89e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16952.95
p-value of test                       :    0.9950



-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.40
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.43
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.02
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.28
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.12
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.48
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.20
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  281.55
p-value of test                       :  1.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.31
p-value of test                       :    0.9955

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.00
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.8e-4    *****

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10415.93
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11581.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12084.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.69
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000193963

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.79
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000013369

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.6e-3

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :   0.091
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.14
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:01.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 C (L=10000, r=15)   1.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56131588.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5587
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    7.91
p-value of test                       :  1.3e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:48.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.57
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.80
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907545
  j =  2                              :            46226
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907780
  j =  2                              :            46107
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    5.83
p-value of test                       :  1.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  7.9e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:15.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9916


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   13.42
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   67.73
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.81
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17595.45
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.95
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.14
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.39
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.53
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.53
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.41
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.63
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.53
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:31.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12265.13
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.25
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999916487

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.20
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000149347

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         : -2.54e-3
p-value of test                       :    0.50

Sample variance                       :    0.21
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:15.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           1.3e-4
 46  MaxOft, t = 8                   7.9e-4
 64  WeightDistrib, r = 26           0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57212932.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4161
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9917

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:49.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.99
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.65
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908461
  j =  2                              :            45765
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908335
  j =  2                              :            45825
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.45e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.18
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.37
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.61
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.59
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.24
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.64
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.40
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4750.59
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.91
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.84
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.80
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999916256

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.51
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999986363

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.093
p-value of test                       :    0.54

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:31.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58261508.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5289
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:19.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     838
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.52
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:46.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.62
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.13
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1565.92
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.53
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.06
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908715
  j =  2                              :            45638
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908129
  j =  2                              :            45931
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17144.62
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.69
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.96
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.01
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.31
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.32
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.71
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.42
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.06
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.54e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.30
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.66
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11534.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.29
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000013978

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.96
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999993536

Normal statistic for number of bits   :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59310084.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.52
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.52
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908080
  j =  2                              :            45954
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908535
  j =  2                              :            45728
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:27.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.69
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.89
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.73
p-value of test                       :    0.9946


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.79
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.43
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.14
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.11
p-value of test                       :    0.9999    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.27
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000044122

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.74
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999990452

Normal statistic for number of bits   :  -0.075
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:56.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60358660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1248
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334368
  j =  1                              :        599997504
  j =  2                              :             1248
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:28.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.68
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.54
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.18
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:29.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.90
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.50
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908512
  j =  2                              :            45738
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907723
  j =  2                              :            46134
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.12
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.46
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.49
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.47
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.41
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  490.23
p-value of test                       :  1.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.47
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.63
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.90
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.65
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.54
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.45e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.86
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.34
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3928.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.48
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999929282

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999983648

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:51.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           0.9993 
 78  RandomWalk1 H (L=10000, r=0)    1.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61407236.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1503
p-value of test                       :  1.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334623
  j =  1                              :        599996994
  j =  2                              :             1503
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1323.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.17
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.36
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5163.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:51.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907907
  j =  2                              :            46039
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908192
  j =  2                              :            45898
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 2.81e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:30.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:30.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.44
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.23
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.14
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.15
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.04
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.93
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.02
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.99
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.27
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.82
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.83
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.05
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  7.1e-4    *****

Anderson-Darling statistic = A2       :    5.16
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  267.98
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.96
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999993068

Normal statistic for number of bits   :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.66
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000050878

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:05.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           1.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 88  PeriodsInStrings, r = 0         9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62455812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.51
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:28.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.56
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4923.30
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:55.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908426
  j =  2                              :            45784
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908066
  j =  2                              :            45964
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.27e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:29.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.94
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.52
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.56
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.91
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.87
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.33
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.79
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.45
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.88
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.03
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.34
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.62
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.56
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.20
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999954524

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.58
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000133153

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:55.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63504388.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7618
p-value of test                       :  2.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.72
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.02
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.87
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.08
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.89
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908325
  j =  2                              :            45830
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45485
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869485
  j =  1                              :        399909036
  j =  2                              :            45473
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:27.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.31
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.30
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.63
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.28
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.10
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.46
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.75
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.04
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.83
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.11
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.37e-4
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.71
p-value of test                       :  7.6e-6    *****

Anderson-Darling statistic = A2       :    7.33
p-value of test                       :  2.6e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.91
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.01
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.87
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000095227

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.98
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999904646

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.70e-4
p-value of test                       :    0.9993    *****

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9913

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:35.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 15  BirthdaySpacings, t = 4         2.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43188244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    4.69
p-value of test                       :  4.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.22
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45551
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869551
  j =  1                              :        399908898
  j =  2                              :            45551
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46193
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870193
  j =  1                              :        399907619
  j =  2                              :            46183
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:28.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.80
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.94
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.36
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.49
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.23
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.88
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    6.20
p-value of test                       :  8.5e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.41
p-value of test                       :    0.9997    *****

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.53e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.22e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.85
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.12
p-value of test                       :  9.9e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9776.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.72
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000014908

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.59
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000053797

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:06.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 83  LempelZiv, r = 15               0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43745305.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    4.90
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7268.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.33
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.67
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907896
  j =  2                              :            46049
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908049
  j =  2                              :            45968
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :  2.9e-4    *****

Anderson-Darling statistic = A2       :    6.50
p-value of test                       :  6.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  6.2e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.59e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.19
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.68
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.47
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.68
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.10
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.40
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.34
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.39
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.13
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.99
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.39
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -403.19
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.21
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.04
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999994661

Normal statistic for number of bits   :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.37
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999804404

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:03.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  6.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45088793.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.72
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.71
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.25
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907541
  j =  2                              :            46225
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908400
  j =  2                              :            45791
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  8.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.74e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:27.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.82
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17076.08
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.40
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.60
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.78
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.85
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  480.70
p-value of test                       :  5.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.60
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.74
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.66
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.81
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999867548

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.19
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000043417

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:55.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 M (L=10000, r=0)    5.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46104601.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7543
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.05
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.87
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5294.31
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908100
  j =  2                              :            45944
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908876
  j =  2                              :            45556
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.56e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17345.47
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.11
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.45
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.70
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.85
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.07
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.20
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.37
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000113584

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.49
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000219409

Normal statistic for number of bits   :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:12.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46956569.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1556.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.31
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.24
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.55
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45720
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869720
  j =  1                              :        399908563
  j =  2                              :            45714
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908240
  j =  2                              :            45874
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :  9.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    4.88
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.92e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17556.30
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.07
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.35
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.28
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.04
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.56
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.60
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.92
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.00
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -8.94e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.38
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000083713

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.66
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999914552

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:21.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48136217.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5238
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.15
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:56.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908058
  j =  2                              :            45962
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46249
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870249
  j =  1                              :        399907504
  j =  2                              :            46245
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.45
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:27.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.45
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17689.52
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.29
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.56
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.95
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.64
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5156.59
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.37
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.94
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.42
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.58
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11555.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.99
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999973544

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.67
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000040957

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:13.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49315865.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5249
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:18.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9907

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.94
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.85
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46146
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870146
  j =  1                              :        399907713
  j =  2                              :            46136
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908159
  j =  2                              :            45916
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.03e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.48
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17752.11
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.25
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.72
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.20
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.02
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.53
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.30
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4828.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5249.58
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.26
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.05
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.77
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.23
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000161635

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.70
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000075217

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:51.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50233369.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.92
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.32
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.44
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.65
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:57.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45759
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869759
  j =  1                              :        399908485
  j =  2                              :            45753
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908046
  j =  2                              :            45971
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.76
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.38
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.08
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.26
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  187.17
p-value of test                       :  2.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.52
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.78
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.14
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.03
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.76
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.54
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.24
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000006469

Normal statistic for number of bits   :   0.051
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.23
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999857207

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.061
p-value of test                       :    0.48

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:25.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51380249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6730.13
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.43
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4916.60
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:55.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908432
  j =  2                              :            45775
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.06e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.46
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17377.19
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.34
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.08
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.08
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.67
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.66
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.62
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.36
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.03
p-value of test                       :    0.9980

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.50
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.53
p-value of test                       :  5.0e-3


-----------------------------------------------
Total number of bits:  8000165529

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.69
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000007291

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:19.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52363289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7121
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7088
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.81
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     963
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9965

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.26
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.79
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908544
  j =  2                              :            45719
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907969
  j =  2                              :            46011
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  9.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.50e-4
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.48e-5
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.34
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.95
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.16
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.97
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.01
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.30
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.44
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.49
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.80
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.21
p-value of test                       :  7.2e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.56
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.27e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.55
p-value of test                       :    0.9918

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.51
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.81
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999976235

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.54
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999962858

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:19.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53280793.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.89
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.02
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.23
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:45.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907708
  j =  2                              :            46143
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908784
  j =  2                              :            45605
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    5.83
p-value of test                       :  1.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :18030.60
p-value of test                       :  7.3e-4    *****



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.36
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.09
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.53
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.39
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -403.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.17
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.62
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.33
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.70
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12124.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.95
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999978866

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.65
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000100273

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:12.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 73  GCD                             7.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54329369.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.28
p-value of test                       :  7.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:27.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.08
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908105
  j =  2                              :            45943
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907755
  j =  2                              :            46121
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17627.55
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.41
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.13
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.43
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.20
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.07
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.23
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.53
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.18
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.21
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.28
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.80
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11491.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.34
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000104197

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.55
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000082498

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.98

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:12.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55803929.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    3.46
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     184
p-value of test                       :  4.0e-3

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1568.85
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.71
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.55
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45447
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869447
  j =  1                              :        399909110
  j =  2                              :            45439
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908494
  j =  2                              :            45750
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9917


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 7.34e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17193.67
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.08
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.89
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.17
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  264.54
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.93
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10289.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.57
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.71
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999959249

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.74
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999948863

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:42.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56623129.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5273
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    3.35
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.14
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.57
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:53.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908026
  j =  2                              :            45981
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908452
  j =  2                              :            45771
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.34
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.73
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.68
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.24
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  203.18
p-value of test                       :  1.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.50
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.72
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  149.57
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.89
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.37
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.63
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9745.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.02
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000070600

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.76
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000008296

Normal statistic for number of bits   :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:28.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57606169.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1485
p-value of test                       :  6.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334605
  j =  1                              :        599997030
  j =  2                              :             1485
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.48
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.90
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.07
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907826
  j =  2                              :            46081
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907794
  j =  2                              :            46097
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
p-value of test                       :    0.9962

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.97
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.52
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.57
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.92
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.05
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.32
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.75
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.02
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000039049

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.33
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999866342

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:22.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            6.5e-4
 24  ClosePairs mNP2S, t = 9         0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58621977.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  376.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.03
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:52.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.30
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5268.27
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46366
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870366
  j =  1                              :        399907269
  j =  2                              :            46364
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908122
  j =  2                              :            45936
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 4.67e-4
p-value of test                       :  1.6e-4    *****

Anderson-Darling statistic = A2       :    5.73
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.20
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17658.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.82
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.19
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.33
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.43
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.08
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.58
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.39
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.64
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.05
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.88
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9755.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.47
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999955664

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000054586

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:18.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59670553.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9954

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:37.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  368.12
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.04
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.89
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908022
  j =  2                              :            45986
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908073
  j =  2                              :            45959
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.89
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.08
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.66
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.12
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.52
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.28
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.41
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.19
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.13
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -402.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:31.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.62
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999967718

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.69
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000034273

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:55.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60719129.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.00
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.45
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.01
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.79
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908072
  j =  2                              :            45964
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908457
  j =  2                              :            45761
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.10e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:19.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.98e-4
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.43
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.96
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.49
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.69
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.67
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.70
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.10
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.06
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.04
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.05
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.13
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.49
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.74
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  4.8e-4    *****

Anderson-Darling statistic = A2       :    4.51
p-value of test                       :  5.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.73
p-value of test                       :  3.1e-3

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.50e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.46e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.68
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.71
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11647.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.31
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999911234

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.65
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000033658

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:33.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61767705.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    4.94
p-value of test                       :  3.1e-3

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  297.58
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.27
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.23
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907751
  j =  2                              :            46114
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908087
  j =  2                              :            45955
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.40e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.79
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.88
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.47
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.22
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.65
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.83
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.60
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.45
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.60
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:23.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.08
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000017368

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.26
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000004306

Normal statistic for number of bits   :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.19
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.48
p-value of test                       :  6.5e-3

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:51.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62816281.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7587
p-value of test                       :  9.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.25
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:28.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.83
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908052
  j =  2                              :            45971
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908249
  j =  2                              :            45871
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.98e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.64
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.65
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.18
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.35
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.42
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.60
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.82
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.15
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  141.53
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.96
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.57e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.63
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.45
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9702.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.45
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :  102.85
p-value of test                       :  7.0e-5    *****


-----------------------------------------------
Total number of bits:  7999867152

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.47
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999930593

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:33.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        9.1e-4
 79  RandomWalk1 C (L=10000, r=15)   0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 101  Run of bits, r = 0              7.0e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43221013.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4115
p-value of test                       :    0.9996    *****


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.34
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:32.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.12
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:56.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907770
  j =  2                              :            46106
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908166
  j =  2                              :            45911
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.56
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.92
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.77
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.16
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.30
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.34
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.93
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.67
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.57
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.51
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.13
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.79
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.74
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-3
p-value of test                       :    0.9987

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    5.60
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10476.00
p-value of test                       :  4.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.20
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.38
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999791879

Normal statistic for number of bits   :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.00
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000077830

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:21.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 90  HammingWeight2, r = 0           4.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43712532.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1502
p-value of test                       :  1.3e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334622
  j =  1                              :        599996996
  j =  2                              :             1502
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:38.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.86
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.92
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908478
  j =  2                              :            45752
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908174
  j =  2                              :            45904
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.27e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 3.46e-4
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.25
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17364.91
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.53
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.86
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.74
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.45
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.09
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.77
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.44
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.22
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.83
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10176.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:32.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.74
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000081307

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.40
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000094078

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:27.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14           1.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44826644.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:29.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.05
p-value of test                       :    0.9950


-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.31
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:54.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45487
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869487
  j =  1                              :        399909028
  j =  2                              :            45483
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908044
  j =  2                              :            45972
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.62e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.34
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.50
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.24
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.07
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.63
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.99
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5173.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.83
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.04
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.45
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.43
p-value of test                       :  2.9e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.84
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4683.74
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.63
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11508.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.98
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000074734

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.96
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000094837

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:00.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45940756.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1497
p-value of test                       :  2.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334617
  j =  1                              :        599997006
  j =  2                              :             1497
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4507
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.95
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    3.75
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6881.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.32
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5205.04
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:53.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908913
  j =  2                              :            45539
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908385
  j =  2                              :            45803
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.99e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.54e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.59
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.31
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.73
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.73
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.70
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.30
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.34
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.26
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4748.58
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.77
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.53
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.17
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.06
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:33.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5052.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.75
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12116.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.34
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999963965

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.41
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999888845

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Tests on the sum of all N observations
Standardized normal statistic         : -7.62e-3
p-value of test                       :    0.50

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.22
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:43.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           2.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47251476.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.60
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6858.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.21
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.01
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907657
  j =  2                              :            46164
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908148
  j =  2                              :            45923
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:27.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.46
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.76
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   66.42
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.22
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.84
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.06
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.22
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.08
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.26
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.13
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.11
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.48e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.69
p-value of test                       :    0.9964

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.79e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.41
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.72
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999910283

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.50
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999902168

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:08.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48300052.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     972
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.45
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.23
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908429
  j =  2                              :            45781
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908255
  j =  2                              :            45865
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
p-value of test                       :    0.9997    *****

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9936


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 3.20e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17499.62
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.55
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.93
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.79
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.96
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.76
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.98
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.98
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4784.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.22
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000039205

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.30
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999920318

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:58.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49348616.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9941


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:45.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   90.90
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908265
  j =  2                              :            45860
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907759
  j =  2                              :            46116
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17172.86
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.73
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.03
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.55
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.38
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.46
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.68
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.36
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.00
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.35
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.79
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000006787

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.92
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999917645

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:17.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50692104.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.07
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46217
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870217
  j =  1                              :        399907569
  j =  2                              :            46211
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908003
  j =  2                              :            45991
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.06e-5
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17494.82
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.38
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.91
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.97
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.60
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.73
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.29
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.89
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.29
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.45
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.31
p-value of test                       :    0.9954

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:35.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.14
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000077290

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.39
p-value of test                       :  7.7e-3


-----------------------------------------------
Total number of bits:  8000114274

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:37.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51740680.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    4.01
p-value of test                       :  8.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9943

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.58
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5292.47
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908514
  j =  2                              :            45734
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908007
  j =  2                              :            45995
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17363.84
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.04
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.70
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.59
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.55
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.00
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.88
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.29
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.17
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.84
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.22
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.65
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.09
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.24
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.43
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.07
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.43
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000002845

Normal statistic for number of bits   :   0.022
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.83
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999962816

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:18.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52756488.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.22
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5209.25
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908731
  j =  2                              :            45633
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907706
  j =  2                              :            46141
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.95
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   16.47
p-value of test                       :  9.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.18
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.83
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.35
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.41
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4696.11
p-value of test                       :    0.9990    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.80
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.18
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11552.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.37
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999991520

Normal statistic for number of bits   :  -0.067
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.80
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999857915

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:34.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 68  MatrixRank, L=1000, r=0         9.1e-4
 79  RandomWalk1 J (L=10000, r=15)   0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53805064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.84
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.28
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.26
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:26.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.54
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908574
  j =  2                              :            45707
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46172
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870172
  j =  1                              :        399907660
  j =  2                              :            46164
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.085
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.03
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.29
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.07
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.61
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.04
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.44
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.67
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.04
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.69
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.45
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.91
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.41
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999878669

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.59
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999944936

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    2.45
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:21.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54689800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.30
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.32
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:55.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907820
  j =  2                              :            46084
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908200
  j =  2                              :            45894
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.61e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.32e-5
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.23
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17256.87
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.94
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.93
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.34
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.19
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.07
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.59
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.31
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.64
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.02
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12194.26
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000209755

Normal statistic for number of bits   :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.13
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000062440

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:22.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           9.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55672855.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5522
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:44.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9939

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:47.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.81
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:22.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45345
p-value of test                       :    0.9937


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869345
  j =  1                              :        399909313
  j =  2                              :            45339
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45787
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869787
  j =  1                              :        399908431
  j =  2                              :            45777
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9902


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  7.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16947.59
p-value of test                       :    0.9954



-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.86
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.54
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.02
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.27
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.65
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.39
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.50
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999955376

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.81
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000034066

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.20

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:08.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57114647.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4530
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.06
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.40
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.41
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4847.78
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45503
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869503
  j =  1                              :        399908998
  j =  2                              :            45495
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908917
  j =  2                              :            45531
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.34
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.19
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.51
p-value of test                       :  5.3e-3


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.90
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.93
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.51
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.22
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.28
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4827.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.45
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.16
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.40
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.14
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.14
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999932357

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.84
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000041074

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58195991.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7086
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.51
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.63
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907861
  j =  2                              :            46062
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.14e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.26
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.21
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17246.21
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.54
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.55
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.41
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.16
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.21
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.84
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.72
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.64
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:31.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4714.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.78
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000015544

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.89
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999947306

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:10.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59244567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:46.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.10
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.22
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5213.18
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46337
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870337
  j =  1                              :        399907333
  j =  2                              :            46323
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908089
  j =  2                              :            45951
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.28e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17355.56
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.93
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.59
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.65
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.44
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.52
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.11
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.80
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999923348

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.16
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000021118

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:07.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60129303.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:46.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    3.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    4.42
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.43
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1343.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.77
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:29.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.92
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.87
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908354
  j =  2                              :            45820
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907824
  j =  2                              :            46088
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.89e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.45
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.83
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.65
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.51
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.11
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.70
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.59
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.68
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.70
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.42
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3892.90
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.52
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000030037

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.36
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000252529

Normal statistic for number of bits   :    2.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:47.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61177879.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.13
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.39
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   58.33
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.74
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.24
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908566
  j =  2                              :            45711
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908540
  j =  2                              :            45724
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.65e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.69
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.25
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.25
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.81
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.28
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.35
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.48
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.71
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.57
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.29
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.75
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.49
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000075241

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.59
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000049177

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:12.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2S, t = 9         0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62226455.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5254
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9975

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:22.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.24
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.97
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908604
  j =  2                              :            45692
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45437
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869437
  j =  1                              :        399909128
  j =  2                              :            45433
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.79e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.74e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.37
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.24
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.19
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.83
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.89
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.81
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.10
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.21
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000000334

Normal statistic for number of bits   : 2.64e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.87
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999979493

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.37

Sample variance                       :    0.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:44.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63242263.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1251
p-value of test                       :    0.9990    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334371
  j =  1                              :        599997498
  j =  2                              :             1251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    3.73
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.77
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.70
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:58.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46169
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870169
  j =  1                              :        399907668
  j =  2                              :            46157
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907796
  j =  2                              :            46096
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.20e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.27
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17712.79
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.73
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.96
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.87
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.90
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   45.98
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.44
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.97
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.08
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  454.83
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.09
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.96
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.70
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10024.08
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.92
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.42
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000126259

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.69
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000007843

Normal statistic for number of bits   :   0.062
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.16

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:27.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43253782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6941.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.30
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.65
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908186
  j =  2                              :            45907
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908302
  j =  2                              :            45846
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:27.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.37
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.13
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17691.55
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.37
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.30
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.25
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.60
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.21
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.51
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.38
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.48
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4805.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.60
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.02
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.49
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.90e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:47.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4665.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.64
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999996839

Normal statistic for number of bits   :  -0.025
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.25
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000054115

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:13.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44138518.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:34.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.33
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.01
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.85
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:03:00.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45500
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869500
  j =  1                              :        399909002
  j =  2                              :            45496
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908208
  j =  2                              :            45896
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.51e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.20e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17360.10
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.59
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.68
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.76
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.60
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.27
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.84
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.78
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.64
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.57
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.38
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.79
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11898.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.31
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999969815

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.84
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000017869

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:52.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45056022.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7536
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.79
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4839.51
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:58.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908189
  j =  2                              :            45901
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907994
  j =  2                              :            45997
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:27.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:27.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17395.74
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.11
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.47
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.89
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.17
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.05
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.14
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.95
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.63
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.65
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.82
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.81
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.49
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.54
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.65
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999974570

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.60
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000148678

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:22.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46366742.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.39
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.63
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.21
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.78
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.33
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.84
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907930
  j =  2                              :            46029
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908452
  j =  2                              :            45765
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.39
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.88
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.82
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.31
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.60
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.62
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.46
p-value of test                       :    0.9920


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.98
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.56
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.68
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4722.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.96
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999917714

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.46
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999946796

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:30.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47415318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.19
p-value of test                       :  7.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7250.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.61
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:31.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.74
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.37
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:54.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908682
  j =  2                              :            45653
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:27.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.91
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.32
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.85
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.91
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.66
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.77
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.90
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.36
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.68
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.05
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.04
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.26
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.22
p-value of test                       :    0.99

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.88
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.43
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.50
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.73
p-value of test                       : 1 -  9.6e-5    *****

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5084.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.03
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.65
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000011848

Normal statistic for number of bits   :   0.094
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.40
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999938753

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:05.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 94  HammingCorr, L = 1200          1 -  9.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48365590.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.54
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.57
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45584
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869584
  j =  1                              :        399908836
  j =  2                              :            45576
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908915
  j =  2                              :            45535
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.90e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:27.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17829.03
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.75
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.55
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.70
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.74
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.52
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.45
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.32
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.66
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.40
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10206.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.39
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000095485

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.72
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000023953

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:16.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49578006.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9933


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    3.51
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     256
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.71
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7235.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.63
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.67
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:53.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908503
  j =  2                              :            45744
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908623
  j =  2                              :            45681
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.17e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17462.98
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.82
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.22
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.11
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.05
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.29
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5182.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.10
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.69
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.91
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.58
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.43
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.08
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  147.99
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.64
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4704.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12201.16
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.18
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000059743

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.87
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000047122

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:47.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50528278.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9972


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.23
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.63
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1295.16
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.36
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.56
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:53.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908359
  j =  2                              :            45810
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908216
  j =  2                              :            45889
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.66e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.79e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.82
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.76
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17360.32
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.25
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.74
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.08
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.99
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.10
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.05
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.22
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.98
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -401.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.76
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999909323

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.13
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000079651

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:51.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51445782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5259
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:12.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1519.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.27
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908462
  j =  2                              :            45763
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908287
  j =  2                              :            45852
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.16e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.00
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17635.80
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.12
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.08
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.46
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.25
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.95
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.77
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.63
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.34
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000171115

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.19
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000057664

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  7.7e-4    *****

Anderson-Darling statistic = A2       :    8.18
p-value of test                       :  1.0e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.86
p-value of test                       :  5.7e-5    *****

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:15.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 105  AutoCor, d=1, r=27              5.7e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52789270.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7541
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.35
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6852.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.09
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45514
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869514
  j =  1                              :        399908979
  j =  2                              :            45500
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.53e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.66e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.92
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.74
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.59
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   58.98
p-value of test                       :  1.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.55
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.11
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.04
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.57
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.48
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.79
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.99
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.28
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.93
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.88
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.60
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999970769

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.63
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999995114

Normal statistic for number of bits   :  -0.039
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.22
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:29.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         0.9991 
 75  RandomWalk1 J (L=50, r=25)      1.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53870614.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.10
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:45.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.19
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.85
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:59.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908303
  j =  2                              :            45844
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.86e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.65
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.98
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.66
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.78
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.87
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.92
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.46
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.63
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.63
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    2.75
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.59e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:34.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.89
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11586.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.25
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999982313

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.18
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999998897

Normal statistic for number of bits   : -8.72e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:54.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54919190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.58
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.52
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:30.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.27
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.17
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:53.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907954
  j =  2                              :            46020
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908301
  j =  2                              :            45845
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17703.06
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.74
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.63
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.63
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.43
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.46
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.89
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.93
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.32
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.39
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.22
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.38
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.50
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.78
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.76
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.062
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4692.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.25
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000012124

Normal statistic for number of bits   :   0.096
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.23
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999878567

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:30.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55869462.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4176
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    3.67
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    4.69
p-value of test                       :  4.1e-3

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.48
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.83
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.09
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908246
  j =  2                              :            45874
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907645
  j =  2                              :            46173
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.18e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17395.88
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.26
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.86
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.15
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.18
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.90
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.14
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.37
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.47
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.87
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.45
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000072436

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.53
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000056980

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    5.15
p-value of test                       :  2.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.14
p-value of test                       :  8.5e-4    *****

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:35.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 105  AutoCor, d=1, r=27              8.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56786952.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    4.17
p-value of test                       :  7.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     119
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:48.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.11
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  512.57
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.23
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.48
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45435
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869435
  j =  1                              :        399909133
  j =  2                              :            45429
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908508
  j =  2                              :            45743
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17472.42
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.70
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.50
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.98
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.20
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.22
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.78
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.90
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.00
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.00
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.12
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.27
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.04
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.21
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.84
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.94
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999953339

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.16
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999922262

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57835528.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9971

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.93
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7150.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:28.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5202.91
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908475
  j =  2                              :            45758
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908068
  j =  2                              :            45963
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.52
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.67
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.12
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.78
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.16
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.22
p-value of test                       :    0.9961


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.34
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.53
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.58
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4794.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.90
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.85
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.89
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.72
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3934.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.96
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999920843

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.45
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999960545

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.063
p-value of test                       :    0.53

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:25.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58818568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7085
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7215.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  9.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   93.33
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.13
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:52.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45554
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869554
  j =  1                              :        399908896
  j =  2                              :            45546
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908385
  j =  2                              :            45806
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-5
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   69.48
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.93
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.02
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.23
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.21
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.67
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.76
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.46
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.91
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.11
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  297.18
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  476.46
p-value of test                       :  4.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.00
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.78
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:32.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.11
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999947726

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.48
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999931871

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:17.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   0.9996 
 79  RandomWalk1 R (L=10000, r=15)   4.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59899912.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.64
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:52.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908317
  j =  2                              :            45837
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45560
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869560
  j =  1                              :        399908884
  j =  2                              :            45552
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.98e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.76
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17131.75
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.28
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.85
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.47
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.12
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.62
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.65
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.39
p-value of test                       :  3.4e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.80
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.38
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11548.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000038791

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.05
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999979895

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60915720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9954

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5212.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:49.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908687
  j =  2                              :            45652
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908342
  j =  2                              :            45826
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.17
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.98
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.21
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.37
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.13
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.89
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.20
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.97
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.50
p-value of test                       :    0.9927

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10232.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5089.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12094.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.20
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000057013

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.56
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999836084

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    2.48
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:12.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62029832.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6817.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:29.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.66
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.16
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908197
  j =  2                              :            45897
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908262
  j =  2                              :            45866
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.07e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.12
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17497.55
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.28
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.36
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.73
p-value of test                       :  7.6e-3


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.32
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.26
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.52
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.80
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.22
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.33
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-3
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10268.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.90
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000086143

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.13
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999973448

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    4.53
p-value of test                       :  5.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:14.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63078408.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.17
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.01
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.39
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:48.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908313
  j =  2                              :            45836
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907922
  j =  2                              :            46036
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.30e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:28.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.24
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.38
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.11
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.63
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.33
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.56
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  200.20
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.45
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.43
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  456.67
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.17
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.79
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.55
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.05e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.80
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.20
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.28
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999807242

Normal statistic for number of bits   :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.40
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000126544

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:37.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43286551.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.99
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4849.74
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908351
  j =  2                              :            45823
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46225
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870225
  j =  1                              :        399907555
  j =  2                              :            46215
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17371.90
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.68
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.92
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.57
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.92
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.64
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.64
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.03
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.54
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.64
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.71e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.33
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999871628

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.87
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999918305

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.19
p-value of test                       :    0.99

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.21
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:09.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44204055.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5311
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7539
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.90
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.33
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7226.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.59
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.87
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.98
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908019
  j =  2                              :            45983
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908236
  j =  2                              :            45873
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:29.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.15
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.82
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.79
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.81
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.17
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.14
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.78
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.59
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.14
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.01e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.97
p-value of test                       :  7.2e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.83
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9683.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10318.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  7.8e-4    *****

Anderson-Darling statistic = A2       :    5.08
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5156.63
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12040.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.64
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999994766

Normal statistic for number of bits   :  -0.041
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.33
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999958487

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:55.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45187095.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.68
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.80
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.33
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908160
  j =  2                              :            45911
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907694
  j =  2                              :            46150
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.05e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   12.35
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.91
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.83
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.67
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.48
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.23
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.94
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.05
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.88
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.50
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.23
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.17
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.34
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.78
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.72
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:03:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.33
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000010330

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.78
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000050848

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:59.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46039043.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:48.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.45
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5230.32
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:53.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908062
  j =  2                              :            45963
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908104
  j =  2                              :            45942
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:14.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.96
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17678.54
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.52
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.58
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.53
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.63
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.75
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.06
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.15
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.32
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.32
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.40
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9709.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12147.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.47
p-value of test                       :  7.6e-3


-----------------------------------------------
Total number of bits:  7999935747

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.19
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000127168

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:22.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47316995.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1218
p-value of test                       : 1 -  3.0e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334338
  j =  1                              :        599997564
  j =  2                              :             1218
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5500
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    3.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.49
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907896
  j =  2                              :            46049
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907948
  j =  2                              :            46020
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:14.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17176.76
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.23
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.28
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.99
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.90
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.15
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   35.79
p-value of test                       :  3.5e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.13
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.89
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
p-value of test                       : 1 -  6.5e-5    *****

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.48
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000002611

Normal statistic for number of bits   :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.39
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999899921

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:55.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  3.0e-5
 80  LinearComp, r = 0              1 - eps1
 80  LinearComp, r = 0               3.5e-4
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48693251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9946


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9918

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    4.79
p-value of test                       :  3.6e-3

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:47.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.49
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:48.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1630.73
p-value of test                       :  2.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6825.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.96
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.38
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908574
  j =  2                              :            45707
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :  2.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    6.31
p-value of test                       :  7.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.52e-5
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17268.10
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.50
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.70
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.61
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.13
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  252.60
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.85
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:35.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3737.60
p-value of test                       : 1 -  8.2e-6    *****

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.44
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999944900

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.06
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000032674

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:32.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                      2.6e-4
 48  MaxOft AD, t = 24               7.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 97  HammingIndep, L=300, r=0       1 -  8.2e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49774595.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9990

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.02
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4909.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907753
  j =  2                              :            46119
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908462
  j =  2                              :            45766
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.28
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.21
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.26
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.56
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.88
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.72
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.45
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.64
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.28
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.55
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.78
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.75
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.14
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.33
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000039919

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.64
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000238570

Normal statistic for number of bits   :    1.89
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:55.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50823171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.94
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4831.57
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908385
  j =  2                              :            45803
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908484
  j =  2                              :            45752
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.60
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.29
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.20
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.76
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.72
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.22
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.08
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.71
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.90
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.04
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.46
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.32
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12175.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.74
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000121519

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.83
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000035161

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:08.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51773443.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:45.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7256.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.79
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.42
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908696
  j =  2                              :            45646
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908638
  j =  2                              :            45672
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:11.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.9e-4    *****

Anderson-Darling statistic = A2       :    4.79
p-value of test                       :  3.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17379.09
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.92
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.97
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.90
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.59
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.40
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.61
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.89
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.75
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.84
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4316.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.85
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000088087

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.62
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000000346

Normal statistic for number of bits   : 2.74e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:33.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52822019.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.46
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  162.33
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.03
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:46.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46347
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870347
  j =  1                              :        399907310
  j =  2                              :            46339
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908394
  j =  2                              :            45794
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.98e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17612.09
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.55
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.27
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.54
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.45
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.30
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.99e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.37
p-value of test                       :    0.9947

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4660.18
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000035848

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.25
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000110689

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:14.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53837827.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    4.61
p-value of test                       :  4.4e-3

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:48.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:28.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.22
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:55.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908149
  j =  2                              :            45924
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908613
  j =  2                              :            45692
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.62
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.82
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.75
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.97
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.33
p-value of test                       :  9.6e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.71
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10284.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.21
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999950561

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.83
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999958331

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:15.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54853635.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.66
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.08
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1328.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   81.58
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4880.36
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:50.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45472
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869472
  j =  1                              :        399909058
  j =  2                              :            45468
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45524
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869524
  j =  1                              :        399908955
  j =  2                              :            45518
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.48
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   63.41
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   39.41
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.00
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.22
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.14
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.49
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.64
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.51
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.81
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.20
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.66
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -3.29
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999987356

Normal statistic for number of bits   :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.68
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000077788

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:22.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 94  HammingCorr, L = 1200           0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55967747.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.91
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:46.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.44
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:29.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.78
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:53.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907898
  j =  2                              :            46042
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907801
  j =  2                              :            46092
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.24
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.10
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.27
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.39
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.81
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.90
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.41e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.54
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:00.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.60
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:34.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11554.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.92
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000094606

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.83
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000057766

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:14.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56950787.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    3.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.44
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.13
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7155.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.01
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.37
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.31
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908440
  j =  2                              :            45771
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908251
  j =  2                              :            45870
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.21
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17216.60
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.05
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.85
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.73
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.26
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.00
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.82
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.69
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.09
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.98
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.67
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.78
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999863879

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.64
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999963515

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.026
p-value of test                       :    0.49

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:16.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57999363.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9915

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.27
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:29.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.68
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46138
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870138
  j =  1                              :        399907728
  j =  2                              :            46130
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907792
  j =  2                              :            46098
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:11.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.49
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.53
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.95
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.97
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.09
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.06
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.33
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.50
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.99
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.37
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.19
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.33
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.12
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999961274

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.29
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999899744

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    2.40
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:57.46
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58982403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4184
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:46.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9983


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6809.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.41
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.71
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46227
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870227
  j =  1                              :        399907547
  j =  2                              :            46225
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 3.66e-4
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.66
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.30
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17585.53
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.15
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.10
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.80
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   44.96
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.46
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.03
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.00
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.75
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.91
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.43
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.28
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.45
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.41
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999981884

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.28
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000040120

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:58.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60260355.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:45.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    4.70
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9989

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.03
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:29.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.52
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908035
  j =  2                              :            45975
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45581
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869581
  j =  1                              :        399908841
  j =  2                              :            45575
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:53.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.14
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.97
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.45
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.69
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.72
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.17
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.61
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.92
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.76
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.78
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.74
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.85
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.85
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.09e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.45
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.54
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12126.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.27
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999990278

Normal statistic for number of bits   :  -0.077
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.44
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999819425

Normal statistic for number of bits   :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         : 1.00e-4
p-value of test                       :    0.50

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:46.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61210627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7041
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.56
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4900.30
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908527
  j =  2                              :            45735
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45558
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869558
  j =  1                              :        399908884
  j =  2                              :            45558
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17683.96
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.68
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.37
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.67
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.68
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.58
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.35
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.08
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.48
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.91
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.34
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.25
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9663.88
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5058.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.96
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000028720

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.53
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999890780

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62291971.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:28.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:19.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.66
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908066
  j =  2                              :            45958
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907983
  j =  2                              :            46004
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-4
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    : 4.05e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17272.21
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.16
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.58
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.50
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.93
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  200.84
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.00
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.47
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.49
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.26
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.96
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.66
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-4
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.98
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  7.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9625.58
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 6.66e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.39
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.41
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000112906

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.60
p-value of test                       :  4.9e-3


-----------------------------------------------
Total number of bits:  7999884303

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:45.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63406083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5319
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.24
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:29.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.52
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4804.42
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908018
  j =  2                              :            45985
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46241
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870241
  j =  1                              :        399907523
  j =  2                              :            46231
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:15.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:15.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.24
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.04
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.46
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.39
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.69
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.02
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.49
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.44
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.65
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.96
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.63
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11561.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.29
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000141895

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.24
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000076282

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.60
p-value of test                       :  4.6e-3

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:55:20.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43319320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:34.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:46.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.66
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.27
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.74
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.14
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45526
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869526
  j =  1                              :        399908951
  j =  2                              :            45520
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908171
  j =  2                              :            45907
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 4.32e-4
p-value of test                       :  5.8e-4    *****

Anderson-Darling statistic = A2       :    6.01
p-value of test                       :  9.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:15.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.76
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.40
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.20
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.41
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.96
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.10
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.96
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.08
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.68
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.56
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.88
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.12
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.04
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000008746

Normal statistic for number of bits   :   0.069
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.23
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000167641

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:26.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              9.8e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44597272.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7058
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:02:49.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.62
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.82
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908643
  j =  2                              :            45668
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907885
  j =  2                              :            46053
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:14.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.01
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.88
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  598.17
p-value of test                       :  1.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.28
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.44
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.24
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.54
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.70
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:32.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.84
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.26
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.18
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.87
p-value of test                       :    0.9989

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.79
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:37.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.52
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.62
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000038350

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.25
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999953564

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:00.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45645848.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:47.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.36
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5271.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45583
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869583
  j =  1                              :        399908837
  j =  2                              :            45577
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907860
  j =  2                              :            46064
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.90e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17103.81
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.58
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.27
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.26
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.35
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.22
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.86
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.46
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.46
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.20
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.71
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -403.09
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.73
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.85
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.39
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999887291

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.36
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999905789

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:50.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46694424.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.33
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.29
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5197.67
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907961
  j =  2                              :            46015
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908441
  j =  2                              :            45769
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.00e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:14.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.87
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   40.53
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.05
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.99
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.02
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.86
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.42
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.56
p-value of test                       :  9.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.18
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.03
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.69
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.63
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.88
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.01
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.17
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.14
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.54
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.98
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000045076

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.99
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000121162

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.22
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:32.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft AD, t = 32               0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47743000.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5546
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.35
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.30
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:59.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907695
  j =  2                              :            46148
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908476
  j =  2                              :            45759
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.72e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:14.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.56
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.16
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.80
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.74
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.90
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.72
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.09
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.57
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.39
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.43
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.34
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.02
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.01e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.60
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  262.11
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.95
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999940679

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.71
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000016324

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:15.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48758808.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:48.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.55
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.97
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.38
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45953
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869953
  j =  1                              :        399908099
  j =  2                              :            45943
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46310
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870310
  j =  1                              :        399907382
  j =  2                              :            46306
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17164.56
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.68
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.14
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.92
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.35
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.55
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.52
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.93
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.92
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.54
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.45
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.44
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999847715

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.88
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999975410

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.34
p-value of test                       :  9.6e-3

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:02.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49807384.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7146
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:16.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    3.52
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.36
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.13
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4852.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:24.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908593
  j =  2                              :            45702
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908224
  j =  2                              :            45882
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:14.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17549.71
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.29
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.45
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.91
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4776.53
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.33
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  267.75
p-value of test                       :  9.7e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:32.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.60
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   30.86
p-value of test                       :  1.5e-4    *****

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.67
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.98
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999860273

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.09
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999977408

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:57.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 C (L=10000, r=15)   9.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 86  LongestHeadRun, r = 0           1.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50888728.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    3.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.85
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:52.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.17
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  492.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.27
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:28.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.15
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.20
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908029
  j =  2                              :            45981
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908584
  j =  2                              :            45705
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17446.39
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.18
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.16
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.86
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.95e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.24
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.43
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000077836

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.39
p-value of test                       :    0.9914


-----------------------------------------------
Total number of bits:  8000026344

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:19.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51970072.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9959

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:28.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.28
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.30
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907619
  j =  2                              :            46180
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908204
  j =  2                              :            45895
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 2.16e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.77
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.97
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.24
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.00
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.65
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.11
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.09
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.11
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5235.25
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.38
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.55
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.70
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.13
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -3.95e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.37
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.80
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000003757

Normal statistic for number of bits   :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.79
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000049858

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:56.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53018648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:36.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.31
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:28.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.15
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.91
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:00.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46202
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870202
  j =  1                              :        399907599
  j =  2                              :            46196
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908092
  j =  2                              :            45951
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.60
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17112.01
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.95
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.60
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.10
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.34
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.97
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.36
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.81
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.97
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.41
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000007423

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.82
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000034192

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         : 4.92e-3
p-value of test                       :    0.50

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:51.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54034456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:17.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    4.05
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:02:50.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.71
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    5.24
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   57.72
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:28.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.41
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4942.94
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:59.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908283
  j =  2                              :            45854
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908465
  j =  2                              :            45763
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.80
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.05
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.43
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.59
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.16
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.53
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.64
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.98
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.45
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.49
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.71e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.27
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:36.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.28
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999972800

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.20
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000009775

Normal statistic for number of bits   :   0.077
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.71
p-value of test                       :  3.4e-3

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:29.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55050264.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.81
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7154.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.80
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:29.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.62
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.75
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908708
  j =  2                              :            45643
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908825
  j =  2                              :            45586
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.30
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.96
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.94
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.36
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.50
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5184.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.57
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.30
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.95
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.024
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5141.10
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.23
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999936305

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.80
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000031966

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:46.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56066072.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7548
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:29.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.19
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908561
  j =  2                              :            45709
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45423
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869423
  j =  1                              :        399909161
  j =  2                              :            45409
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.41e-4
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  179.30
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17196.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.77
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.46
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.68
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.18
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.54
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.36
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.07
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.36
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.60
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.14
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.59
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.65
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000134371

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.11
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999987512

Normal statistic for number of bits   :  -0.099
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.25
p-value of test                       :    0.99

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:17.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57081880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.56
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.91
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908553
  j =  2                              :            45722
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908506
  j =  2                              :            45744
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.84
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17042.82
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.81
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.70
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.81
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.02
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.14
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.74
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.46
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.31
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.23
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.69
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9806.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:33.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.66
p-value of test                       :  4.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4620.41
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.71
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999934034

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.34
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000065689

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:20.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58130456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:46.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.32
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.69
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908453
  j =  2                              :            45766
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908204
  j =  2                              :            45898
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.68e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.62
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.71
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.03
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.88
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.45
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.41
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.84
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.27
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.62
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.41
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.88
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.01e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.87
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.85
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:32.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.76
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.84
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000082213

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.38
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000004465

Normal statistic for number of bits   :   0.035
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:20.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59113496.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.92
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.98
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:47.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907858
  j =  2                              :            46062
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45460
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869460
  j =  1                              :        399909082
  j =  2                              :            45456
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    5.30
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.38
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17865.63
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.88
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.52
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.85
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  573.79
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.51
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.33
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.12
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.15
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.83
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.34
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.98
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.06
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.14
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999963320

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.97
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000129181

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  1.9e-4    *****

Anderson-Darling statistic = A2       :    5.34
p-value of test                       :  2.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.73
p-value of test                       :  3.2e-3

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:42.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60063768.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:46.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    4.07
p-value of test                       :  8.0e-3

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    4.42
p-value of test                       :  5.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     345
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7248.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.15
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:29.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.81
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45452
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869452
  j =  1                              :        399909096
  j =  2                              :            45452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908619
  j =  2                              :            45689
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:31.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.35
p-value of test                       :  6.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.31
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17645.71
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.13
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.96
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  421.36
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.90
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.15
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.27
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.28
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.21
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.41e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.95
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.42
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4714.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12376.47
p-value of test                       :  2.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11608.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.97
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999979028

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.47
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000083119

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:07.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 99  HammingIndep, L=1200, r=0       2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61079576.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9982

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5215.29
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908183
  j =  2                              :            45904
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908641
  j =  2                              :            45678
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:34.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.83
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.52
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  200.01
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.50
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.76
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.17
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.06
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.87e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.56
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999937955

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.22
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999887090

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:53.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62193688.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:28.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    3.45
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     996
p-value of test                       :  8.6e-4    *****

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9956

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.95
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.78
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.16
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.51
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4921.20
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:53.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908176
  j =  2                              :            45903
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46190
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870190
  j =  1                              :        399907623
  j =  2                              :            46184
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17184.29
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.24
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.80
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.06
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.43
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.88
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.49
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5269.65
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.83
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.99
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.44
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000065152

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.38
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000162592

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  1.0e-2

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:31.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NJumps, t = 3        8.6e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63307800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.04
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:28.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.11
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:56.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908022
  j =  2                              :            45983
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907786
  j =  2                              :            46098
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:27.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:28.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.21
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.30
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.83
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.13
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.61
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.45
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -403.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.93e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.20e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.68
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000099949

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.76
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999992864

Normal statistic for number of bits   :  -0.056
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.23
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:28.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43352089.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:22.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.34
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.53
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908004
  j =  2                              :            45992
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908697
  j =  2                              :            45650
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:09.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.24e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.60
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.83
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.37
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.53
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.71
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.60
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.62
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.40
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.62
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  467.19
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.31
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.14
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.88
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.31
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.97
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 7.56e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.59
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.71
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.70
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999802790

Normal statistic for number of bits   :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.59
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999933557

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:19.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43679765.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:20.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    3.47
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:46.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.60
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908578
  j =  2                              :            45708
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908276
  j =  2                              :            45859
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.73e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:14.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:27.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.44
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17286.63
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.01
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.44
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.93
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.52
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.50
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.22
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5053.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.62
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000056152

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.52
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000083788

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:40.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45482005.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:47.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7558
p-value of test                       :  2.7e-3


-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    5.40
p-value of test                       :  1.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     822
p-value of test                       :    0.9956

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  503.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.45
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.91
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908526
  j =  2                              :            45731
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46111
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870111
  j =  1                              :        399907780
  j =  2                              :            46107
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9919


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.21e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.51
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.77
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.03
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.21
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.67
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.80
p-value of test                       :    0.9992    *****

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.47
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999803609

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.04
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000067840

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:17.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 87  LongestHeadRun, r = 27          0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46628885.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    6.71
p-value of test                       :  4.7e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    5.72
p-value of test                       :  1.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     122
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1582.28
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:30.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.84
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.79
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908182
  j =  2                              :            45903
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45626
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869626
  j =  1                              :        399908753
  j =  2                              :            45616
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.44e-6
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:14.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:27.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17606.38
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.66
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.38
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.80
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.94
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.38
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.40
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.04
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.55
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.19
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.05
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.11
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -403.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  1.0e-2

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.94
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5108.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.49
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999921434

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.54
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999850661

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    3.27
p-value of test                       :  5.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:08.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          4.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47677461.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5563
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7079
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:09.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.13
p-value of test                       :  8.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7202.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.68
p-value of test                       :  3.8e-3

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.84
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:29.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.18
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.32
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45322
p-value of test                       :    0.9954


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869322
  j =  1                              :        399909358
  j =  2                              :            45318
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908284
  j =  2                              :            45849
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  7.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.25e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.73e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.08
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.06
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.23
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.42
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.81
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.96
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.75
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.85
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -401.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.50e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.83
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.28
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10277.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:35.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.42
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3922.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.41
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999977936

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.91
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000036130

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.01

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:33.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48627733.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7141.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:30.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.14
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.44
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908549
  j =  2                              :            45721
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907993
  j =  2                              :            45999
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:28.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   75.84
p-value of test                       :  1.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17180.17
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.46
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.54
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.65
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.11
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.52
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.74
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.94
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.72
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.39
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.96e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:35.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.09
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999966077

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.32
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999932489

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:39.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            1.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49643541.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:45.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.70
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.27
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908611
  j =  2                              :            45687
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908122
  j =  2                              :            45930
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.54e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -9.98e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17660.19
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.92
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.29
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.11
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.48
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.69
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.10
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.83
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.39
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.01
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.10
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.48
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.45
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.21
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.78
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.52
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999835994

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.50
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000038377

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.061
p-value of test                       :    0.52

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:37.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50659349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.13
p-value of test                       :    0.9996    *****

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    4.51
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.31
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.17
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908467
  j =  2                              :            45762
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908193
  j =  2                              :            45899
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.17e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17217.10
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.33
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.51
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.87
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.65
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.00
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.46
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.42
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.61
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.70
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.77
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.18
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3851.02
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.48
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999983399

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.37
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000134026

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:59.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51675157.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    3.82
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     533
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7290.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  101.12
p-value of test                       :  7.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.91
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:02.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908377
  j =  2                              :            45807
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  2.3e-4    *****

Anderson-Darling statistic = A2       :    5.80
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17452.80
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.98
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.61
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.66
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.15
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.71
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.11
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4817.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.03
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.23
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:08.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.27
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:34.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.14
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999911534

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.33
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000071941

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:18.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     7.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52723733.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:34.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4491
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    3.23
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.84
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.90
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908608
  j =  2                              :            45690
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907888
  j =  2                              :            46053
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.64
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.32
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    : 3.98e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   91.25
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17679.12
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.60
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.27
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.38
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.13
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.03
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.35
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.30
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.52
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.61
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.90
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -403.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.40
p-value of test                       :    0.9918

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.84
p-value of test                       :  5.2e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.52
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.04
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.27
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.10
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999993362

Normal statistic for number of bits   :  -0.052
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.67
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999864446

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.061
p-value of test                       :    0.48

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:13.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53706773.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7059
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4481
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:47.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:30.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.85
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.63
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908028
  j =  2                              :            45983
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46156
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870156
  j =  1                              :        399907690
  j =  2                              :            46152
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17583.77
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.93
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.99
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.66
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.14
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.91
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.21
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.93
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.35e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.65
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.55
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000216160

Normal statistic for number of bits   :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000033850

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:09.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54755349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     825
p-value of test                       :    0.9940

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    4.17
p-value of test                       :  7.3e-3

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.01
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5167.88
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907967
  j =  2                              :            46009
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907764
  j =  2                              :            46112
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.43e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:28.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17641.82
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.40
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.79
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.78
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.96
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.29
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.56
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.04
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.76
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.04
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.34
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.86e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.95
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.11
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4269.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.91
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999946739

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.73
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000015739

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:57.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55705621.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:37.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:29.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.76
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:46.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908449
  j =  2                              :            45774
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907858
  j =  2                              :            46068
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.65
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.97
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.38
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.07
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.93
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.42
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.10
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.20
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.49
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.81
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.09
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  257.26
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.51
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999944081

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.69
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000055717

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:10.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56721429.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.02
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     960
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.77
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.80
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:53.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45627
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869627
  j =  1                              :        399908750
  j =  2                              :            45619
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908119
  j =  2                              :            45936
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.93
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.28
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.52
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.58
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.30
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.27
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.86
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.36
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.46
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.92
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.15
p-value of test                       :  2.6e-3


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.83
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.13
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.76
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9762.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4671.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.69
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000049927

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.69
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999829211

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.15e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    : 1.82e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  3.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.04
p-value of test                       :    0.9988

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:14.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57638933.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:34.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1321.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.18
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.21
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.42
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908048
  j =  2                              :            45970
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908432
  j =  2                              :            45778
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17615.18
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.02
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.95
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.99
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.86
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.44
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.46
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.23
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.64
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.64
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.81
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.08
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.30e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.36
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.76
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.94
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10377.89
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.76
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000119779

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.26
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000146227

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:04.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58884117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9954

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:48.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:26.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.76
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.01
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46244
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870244
  j =  1                              :        399907517
  j =  2                              :            46234
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907814
  j =  2                              :            46084
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.55
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.15
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.71
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.36
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.30
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.29
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.38
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.88
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.41
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.17
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.85
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.19
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.84
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.95
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.32
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.31
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12304.92
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.99
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999971879

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.14
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999969863

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:12.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59703317.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:33.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    5.66
p-value of test                       :  1.4e-3

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.41
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908102
  j =  2                              :            45943
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908546
  j =  2                              :            45724
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.08
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17126.83
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.83
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.64
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.68
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.47
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.18
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.94
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.99
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.24
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.73
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.40
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.54
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:30.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.96
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.90
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999937430

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.15
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999976046

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.27
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60784661.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    3.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.05
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.64
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4935.35
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907772
  j =  2                              :            46108
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908599
  j =  2                              :            45699
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-5
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    : 3.81e-4
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    5.14
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.05e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.17
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.23
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.89
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.52
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.69
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.41
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  450.96
p-value of test                       :  5.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.47
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.53
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.94
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -403.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 3.58e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  253.09
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.73e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4303.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.98
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000020935

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.54
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999950519

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:54.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61800469.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.93
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.97
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.31
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.49
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45681
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869681
  j =  1                              :        399908641
  j =  2                              :            45675
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45523
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869523
  j =  1                              :        399908956
  j =  2                              :            45519
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.032
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:30.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17861.70
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.83
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.00
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.40
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.75
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.51
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.75
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.22
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10129.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:24.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.35
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999954815

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.43
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999903767

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    3.05
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:24.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62849045.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.76
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.33
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.18
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5217.96
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908476
  j =  2                              :            45756
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908037
  j =  2                              :            45974
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.84
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:28.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.14
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.46
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.12
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.14
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.27
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.90
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4776.07
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.43
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.18
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.38
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.98
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -401.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.21
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.91
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999938996

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.20
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999859016

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:53.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43384858.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7526
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1569.74
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.14
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:52.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907923
  j =  2                              :            46037
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907868
  j =  2                              :            46060
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9949

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 3.55e-4
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  107.85
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:28.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17603.00
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.09
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.67
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.94
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.26
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.04
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.01
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.71
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.74
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.83
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.08
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:47.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:35.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4662.88
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.41
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999997511

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.49
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999941459

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.068
p-value of test                       :    0.53

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:07.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43876378.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.26
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    3.53
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.30
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.98
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  488.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.33
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.71
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:48.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908474
  j =  2                              :            45760
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45561
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869561
  j =  1                              :        399908881
  j =  2                              :            45555
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.38
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.14
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.01
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.32
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.35
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.05
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.77
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.86e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:32.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.01
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.51
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999993938

Normal statistic for number of bits   :  -0.048
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.59
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999855386

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.46
p-value of test                       :  6.9e-3

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:33.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44859418.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7067
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    2.76
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:37.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.69
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:32.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.04
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:47.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908314
  j =  2                              :            45843
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908449
  j =  2                              :            45771
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:29.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.38
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.51
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.72
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.30
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.80
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.84
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.95
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.03
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.68
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.78
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.26
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.40
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.29
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.24
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.26
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    2.57
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.27
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10233.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.27
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999907181

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.88
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000193570

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:28.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9995 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45842458.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:38.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.07
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.80
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4765.84
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:52.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908565
  j =  2                              :            45716
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907620
  j =  2                              :            46187
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.89e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.79
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.74
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17685.28
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.80
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.75
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.04
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.03
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.85
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.60
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.19
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.70
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.27
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.22
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.12
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999971642

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.97
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000100237

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:36.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46825498.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7055
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.87
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    4.18
p-value of test                       :  7.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     976
p-value of test                       :  6.4e-3

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     343
p-value of test                       :  8.0e-3

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.69
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.02
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.72
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:54.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908268
  j =  2                              :            45863
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908378
  j =  2                              :            45802
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.32e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.39
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.58
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.68
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.29
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.13
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5348.41
p-value of test                       :  3.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.96
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.00
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.79
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.81
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.15
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.15
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.47
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4356.68
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.30
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999947861

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.62
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000013693

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:32.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 J (L=10000, r=0)    3.2e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47906842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    4.75
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.58
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.31
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.56
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:52.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45004
p-value of test                       : 1 -  2.1e-5    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869004
  j =  1                              :        399909994
  j =  2                              :            45000
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908691
  j =  2                              :            45647
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17615.04
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.78
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.92
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.34
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.00
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.90
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.92
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.47
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.94
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.88
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.34
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.88
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.63
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.31
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9652.74
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.77
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999958193

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.17
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000052276

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:24.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0         1 -  2.1e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48988186.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5517
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.76
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.36
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9920


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.55
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:29.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:48.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908454
  j =  2                              :            45770
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908009
  j =  2                              :            45991
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.85
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.27
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.15
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.48
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.08
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.01
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.46
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.08
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.86
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.99
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.85
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.84
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.31
p-value of test                       :    0.01

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.09
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.36
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000031870

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.37
p-value of test                       :    0.9961


-----------------------------------------------
Total number of bits:  8000045022

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:58.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50429978.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    4.46
p-value of test                       :  5.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     665
p-value of test                       :  4.7e-3

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.84
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:31.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.07
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5218.21
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:52.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907793
  j =  2                              :            46093
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908356
  j =  2                              :            45819
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 3.59e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.63
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.40
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.76
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.50
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.79
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.60
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.42
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.12
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.13
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.88
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.24
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.47
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.17
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999968579

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.54
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999990092

Normal statistic for number of bits   :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:09.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51478554.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5193
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7104
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.88
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6871.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.83
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.42
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:48.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908410
  j =  2                              :            45786
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908579
  j =  2                              :            45703
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17610.89
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.88
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.30
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.87
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.67
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.46
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.61e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.05
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.08
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3930.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   29.11
p-value of test                       :    0.9978


-----------------------------------------------
Total number of bits:  7999974027

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.43
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999936611

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:07.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52396058.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997285
  j =  2                              :             1356
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.51
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.98
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.96
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.64
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908591
  j =  2                              :            45688
  j =  3                              :               11
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907855
  j =  2                              :            46062
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.41
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.40
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.46
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.06
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.61
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.52
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.04
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.34
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.82
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.27e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.33
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.81
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.71
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4323.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.76
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999887867

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.03
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000067195

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.74
p-value of test                       :  3.1e-3

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:55.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53379098.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.27
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.87
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.74
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907937
  j =  2                              :            46027
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45675
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869675
  j =  1                              :        399908653
  j =  2                              :            45669
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.31e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.15
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.70
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.17
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.88
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.54
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.58
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.36
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.43
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.28
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.44
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:33.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.23
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4706.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.92
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000011947

Normal statistic for number of bits   :   0.094
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.37
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000173185

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:13.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54427674.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:45.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.73
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7140.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.01
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5212.56
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907757
  j =  2                              :            46117
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908312
  j =  2                              :            45838
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.36e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17799.10
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.22
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.10
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.78
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.11
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.05
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.07
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.0e-3

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12202.85
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.07
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000104161

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.88
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000013129

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.85

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:37.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56098842.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9985


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    4.41
p-value of test                       :  5.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.84
p-value of test                       :  9.1e-5    *****

Anderson-Darling statistic = A2       :    7.24
p-value of test                       :  3.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   58.75
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.49
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.96
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4842.60
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908559
  j =  2                              :            45716
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908636
  j =  2                              :            45679
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 3.25e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.73
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.24
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.12
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.52
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.32
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.63
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.21
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.86
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.28
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.59
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.09
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.37
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.87
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000131446

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.00
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999887429

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:02.84
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57049114.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.97
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.56
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45604
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869604
  j =  1                              :        399908794
  j =  2                              :            45600
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908241
  j =  2                              :            45878
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:27.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.00
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.27
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.54
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.55
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  303.40
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.88
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.01
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.09
p-value of test                       :    0.9948


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.47
p-value of test                       :    0.9999    *****

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.51
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3941.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12143.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.52
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000125236

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.09
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000030709

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:24.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 86  LongestHeadRun, r = 0           0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58097690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:35.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.37
p-value of test                       :  6.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.70
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:29.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.57
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.80
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46336
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870336
  j =  1                              :        399907332
  j =  2                              :            46328
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908885
  j =  2                              :            45553
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:10.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.39e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.98
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   16.57
p-value of test                       :  8.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.22
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.53
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.39
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.21
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.89
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.47
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.73
p-value of test                       :    0.9948


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.16
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.01e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9884.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.16
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.27
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000025963

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.52
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000209482

Normal statistic for number of bits   :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.019
p-value of test                       :    0.51

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:59.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 69  MatrixRank, L=1000, r=26        8.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59080730.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    3.83
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.29
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.59
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.99
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.42
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.91
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45990
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869990
  j =  1                              :        399908024
  j =  2                              :            45982
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907907
  j =  2                              :            46042
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.9900

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:15.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.66
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.12
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.00
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.73
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.28
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.45
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.75
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 3.77e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:31.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.96
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999951224

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.78
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000043759

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:34.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60096538.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.59
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1549.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.70
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.65
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908431
  j =  2                              :            45780
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907861
  j =  2                              :            46065
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:09.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:20.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 9.60e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.74
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.75
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.05
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.86
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.40
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.11
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.73
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.44
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.32
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.27e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.38
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.89
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999812327

Normal statistic for number of bits   :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.29
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000003793

Normal statistic for number of bits   :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:17.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61112346.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:12.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.76
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:02.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907823
  j =  2                              :            46081
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907841
  j =  2                              :            46075
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-5
p-value of test                       :    0.9900

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.91
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.81
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.83
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.29
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.84
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.72
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.33
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.09
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.30
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.57
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.39
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.15
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.20
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000023506

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.58
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999949064

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              0.9990 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62128154.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:28.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.04
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.81
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908234
  j =  2                              :            45874
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908613
  j =  2                              :            45689
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    5.11
p-value of test                       :  2.6e-3


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.73e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17688.80
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.59
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.39
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.56
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.90
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.98
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.68
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.08
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.92
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.40
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000042265

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.61
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000144952

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:39:58.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63143962.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.65
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.02
p-value of test                       :  9.4e-3

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.08
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.67
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.45
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908334
  j =  2                              :            45830
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908750
  j =  2                              :            45616
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:28.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.29
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.75
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.84
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.70
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.85
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   96.91
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.48
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.41
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.23
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.87
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.05
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.50
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.63
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.66
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.26
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:47.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11548.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.28
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999887345

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.31
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999975827

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.20
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:46.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 H (L=1000, r=20)    0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43417627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.71
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:37.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.04
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.48
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:46.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908519
  j =  2                              :            45736
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908596
  j =  2                              :            45699
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -3.68e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:27.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17636.71
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.06
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.43
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.56
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.90
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.41
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  112.40
p-value of test                       :  2.7e-3


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.93
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.48
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.80
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.56
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.88
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.05
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:18.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4652.96
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12042.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.32
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000042565

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.56
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000198946

Normal statistic for number of bits   :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:52.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43843611.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.69
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.72
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.90
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45871
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869871
  j =  1                              :        399908261
  j =  2                              :            45865
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908709
  j =  2                              :            45638
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:27.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.20
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.54
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.32
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.82
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.53
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.80
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.77
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.89
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.00
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9743.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5095.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4385.97
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12059.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.77
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000035149

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.42
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999972971

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:51.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45449243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.87
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.36
p-value of test                       :  6.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:38.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.36
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.23
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.19
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:31.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.53
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:48.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907946
  j =  2                              :            46024
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46243
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870243
  j =  1                              :        399907518
  j =  2                              :            46235
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.34e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:27.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17653.40
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.94
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.19
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.40
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  312.79
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.97
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.06
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.82e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.9900

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9616.49
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000006403

Normal statistic for number of bits   :   0.051
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.34
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000108475

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  9.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:52.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45973521.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1232
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334352
  j =  1                              :        599997536
  j =  2                              :             1232
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7300.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:33.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.80
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.79
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46225
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870225
  j =  1                              :        399907551
  j =  2                              :            46223
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908594
  j =  2                              :            45697
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :  1.9e-4    *****

Anderson-Darling statistic = A2       :    7.54
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:20.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:27.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.86
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.84
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.95
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.02
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.33
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4768.74
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.79
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.15
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.48
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -403.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.05e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.74
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.14
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.39
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999890300

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.86
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000150205

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.23e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:58.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9999 
 48  MaxOft AD, t = 24               2.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46923793.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1244
p-value of test                       :    0.9995    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334364
  j =  1                              :        599997512
  j =  2                              :             1244
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4127
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.14
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.55
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.85
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908175
  j =  2                              :            45905
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907874
  j =  2                              :            46060
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.78e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.88
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.79
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.88
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.03
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.99
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.09
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.40
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.78
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.00
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.22
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.31
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.32
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.81
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.84
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999799982

Normal statistic for number of bits   :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999982697

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:09.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9995 
 17  BirthdaySpacings, t = 7         0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47874065.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5569
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7240.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.27
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.41
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.98
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45370
p-value of test                       :    0.9913


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869370
  j =  1                              :        399909263
  j =  2                              :            45364
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908237
  j =  2                              :            45877
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:20.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17755.32
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   46.30
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.87
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  202.35
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.78
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.96
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.15
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.68
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.10
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.73
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.45
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.01
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10267.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.33
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000026932

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.98
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000008473

Normal statistic for number of bits   :   0.067
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:37.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48922641.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.00
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4842.70
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908082
  j =  2                              :            45953
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45486
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869486
  j =  1                              :        399909032
  j =  2                              :            45478
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:20.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.73
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.36
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.41
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.14
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.14
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.00
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  146.49
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.77
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.48
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.27
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.45
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.48
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.61e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.98
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000045823

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.36
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000113182

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:45.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49938449.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.86
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.37
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.52
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.40
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907980
  j =  2                              :            46004
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908868
  j =  2                              :            45566
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.91
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17596.63
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.22
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.63
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.91
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.11
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.78
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.73
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.88
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.37
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.47
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:58.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10360.55
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.39
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:33.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.91
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.51
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999916499

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.90
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000079090

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:04.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50987025.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9978

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.63
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7207.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:33.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.12
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.71
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45493
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869493
  j =  1                              :        399909018
  j =  2                              :            45485
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908776
  j =  2                              :            45609
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.88
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.05
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.97
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.81
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.21
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.99
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.77
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.57
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  311.89
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.45
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.49
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.88
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -403.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.31
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11505.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.49
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000168601

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.64
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999947423

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:46.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52068369.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1558.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7169.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.84
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4919.93
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907695
  j =  2                              :            46148
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908530
  j =  2                              :            45732
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 3.05e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.33
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17216.17
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.03
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.28
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.47
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.86
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.90
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.48
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.41
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.43
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999935723

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.64
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000124807

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    3.30
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:39.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53084177.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7128
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7162.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.58
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.77
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.92
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907897
  j =  2                              :            46041
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908123
  j =  2                              :            45928
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.32e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:12.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.49
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:27.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17687.75
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.49
p-value of test                       :    0.9901


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.21
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.80
p-value of test                       :    0.9907


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.77
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.89
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.54
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.85
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  308.11
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.30
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.18
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : -402.80
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.33
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.15e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.70
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.52
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.057
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.85
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999897809

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.38
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000001963

Normal statistic for number of bits   :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:07.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54132753.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5264
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9985

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1352.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.53
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908382
  j =  2                              :            45803
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908813
  j =  2                              :            45592
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.93e-6
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:30.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.57
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.62
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.81
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.14
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.18
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.09
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.51
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.78
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.99
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.07
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.34
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.19
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.55
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.85
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.99
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999916940

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.60
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999959855

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:21.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55181329.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5305
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4199
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:35.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:21.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.84
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.27
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:56.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908491
  j =  2                              :            45750
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908400
  j =  2                              :            45797
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.95e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:18.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.76e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:29.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:30.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.48
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.49
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.08
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.80
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   90.69
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.94
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.57
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.41
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.83
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.14
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.18
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.65
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : -403.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.81
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.17e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 4.17e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.66
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4319.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.24
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000125974

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.61
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999918581

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.10

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56229905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:36.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    3.24
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.64
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:30.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.56
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4870.49
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45998
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869998
  j =  1                              :        399908005
  j =  2                              :            45996
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908171
  j =  2                              :            45907
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:18.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:12.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:33.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.74
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.09
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.27
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.03
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.26
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.59
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.31
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.77
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.30
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.01
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.34
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.35
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.34
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000005098

Normal statistic for number of bits   :   0.040
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.53
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999931130

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:31.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57311249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.74
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:22.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:30.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.74
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5197.19
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45470
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869470
  j =  1                              :        399909061
  j =  2                              :            45468
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908591
  j =  2                              :            45700
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:29.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:29.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.68
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.98
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17298.06
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.20
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.44
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.89
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.92
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.93
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.25
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.61
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.39
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5252.40
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.21
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.61
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.99
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.92
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.96
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.98
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.08
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.22
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.37
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999903722

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.27
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999890648

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:58.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58425361.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9954

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.91
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:30.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.54
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:57.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907869
  j =  2                              :            46061
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46080
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870080
  j =  1                              :        399907840
  j =  2                              :            46080
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:18.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:19.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:29.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:29.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:29.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:29.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.33
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.00
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.61
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.34
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.95
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.09
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.49
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.00
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.65
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.66
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5221.41
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.06
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.64
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:29.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.75
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11676.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.15
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000079573

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.89
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999964631

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:07.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59473937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    4.82
p-value of test                       :  3.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     346
p-value of test                       :  5.0e-3

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:30.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.23
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.68
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908207
  j =  2                              :            45892
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46180
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870180
  j =  1                              :        399907648
  j =  2                              :            46164
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:19.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.20e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:12.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:28.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:28.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17705.37
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.74
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.55
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.76
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  283.41
p-value of test                       : 1 -  3.4e-5    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.33
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.73
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.55
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.43
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4473.31
p-value of test                       :  6.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.17
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999948230

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.41
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000051097

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:49.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 H (L=10000, r=0)   1 -  3.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 98  HammingIndep, L=300, r=26       6.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60522513.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.80
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:30.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.91
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907838
  j =  2                              :            46078
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908273
  j =  2                              :            45862
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  1.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    6.22
p-value of test                       :  7.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.27e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:13.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.52
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:29.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.44
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.48
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.89
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.96
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.96
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.21
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.12
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.59
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.37
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.10
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.68
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.36
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.57
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.82
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:10.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.31
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12308.92
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.10
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999969998

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.02
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999958364

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         : 8.56e-3
p-value of test                       :    0.50

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:38:20.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft, t = 8                   0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 99  HammingIndep, L=1200, r=0       9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61538321.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5296
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:47.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.30
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908139
  j =  2                              :            45923
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45588
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869588
  j =  1                              :        399908824
  j =  2                              :            45588
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.89
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:31.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.49
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.63
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.18
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.98
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.54
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.91
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.28
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.33
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  483.70
p-value of test                       :  4.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.03
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.02
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.02
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:43.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.80
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999928058

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.50
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999935147

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:37:19.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   4.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62586897.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4500
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.96
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     180
p-value of test                       :  9.4e-3

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.62
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:28.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.94
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4934.31
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908740
  j =  2                              :            45621
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907986
  j =  2                              :            46001
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.36
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17697.58
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.28
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.38
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.22
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  467.26
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.59
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.97
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.71
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.43
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.51
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.44
p-value of test                       :  2.2e-3


-----------------------------------------------
Total number of bits:  8000132730

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.99
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999982229

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:56:54.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43450396.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:45.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.64
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.18
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.61
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6879.82
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.42
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.64
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4896.27
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908610
  j =  2                              :            45692
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908412
  j =  2                              :            45791
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:15.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   68.91
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:31.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17476.88
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.30
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.67
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.95
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.36
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.39
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.85
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.41
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.01
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.12
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.93
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5071.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4384.10
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.45
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000032917

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.66
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999937112

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:01.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44630044.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     124
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.08
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.26
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.60
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45643
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869643
  j =  1                              :        399908718
  j =  2                              :            45635
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908325
  j =  2                              :            45836
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.73e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:15.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.61
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.98
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.75
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.12
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.76
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.91
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.81
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.95
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.28
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.48
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.40
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.89
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.61
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    4.07
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4668.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.18
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999838793

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.81
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999990686

Normal statistic for number of bits   :  -0.074
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:18.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45678620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.39
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:10.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1544.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:29.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.67
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.29
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908142
  j =  2                              :            45923
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908085
  j =  2                              :            45944
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:14.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17471.74
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.10
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.33
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.02
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.01
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4807.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.56
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.55
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.04
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.95
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.37
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999971333

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.00
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000023941

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:16.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46661660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:15.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.43
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.07
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.63
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:22.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.35
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.45
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.04
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46458
p-value of test                       :  3.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870458
  j =  1                              :        399907086
  j =  2                              :            46454
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908757
  j =  2                              :            45617
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.47
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17628.61
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.67
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.83
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4746.40
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.55
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.27
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.05
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.94
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.07
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.33e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.09
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999872270

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.60
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000130114

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:32.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47710236.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:29.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.29
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5169.51
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908469
  j =  2                              :            45755
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908753
  j =  2                              :            45619
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:14.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:14.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.32
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17238.67
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.32
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   48.78
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.73
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.41
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.52
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.93
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.59
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.78
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.23
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.66
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.16
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.65
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.14
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   34.17
p-value of test                       :  6.4e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  : -403.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.94
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.25
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.05
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11499.92
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.40
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000009037

Normal statistic for number of bits   :   0.071
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.51
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000158608

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.23
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:47.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 81  LinearComp, r = 0               6.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48726044.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5304
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.14
p-value of test                       :  7.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.56
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1582.56
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:29.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.63
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5256.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45555
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869555
  j =  1                              :        399908892
  j =  2                              :            45551
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908224
  j =  2                              :            45885
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.06e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:26.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.71
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.63
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.70
p-value of test                       :    0.9934


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.66
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.51
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.35
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.17
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.07
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5254.08
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.84
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.53
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.03e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.41
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.52
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11581.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.57
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000072607

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.07
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000064972

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:42.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49741852.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9908


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:11.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   91.99
p-value of test                       :  9.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:29.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.24
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907978
  j =  2                              :            46011
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907977
  j =  2                              :            46007
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17237.81
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.84
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.09
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.88
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.87
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.82
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.17
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4808.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.17
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.48
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.30e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.78
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.76
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.98
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000095257

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.36
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999959696

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:34.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         9.7e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50790428.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4481
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:02:42.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.82
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.87
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908613
  j =  2                              :            45683
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46354
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870354
  j =  1                              :        399907296
  j =  2                              :            46346
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.11
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.57
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.62
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.30
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.77
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.89
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.38
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.31
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.57
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.75
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999968906

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.36
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000179845

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:20.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51839004.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.72
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:47.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.42
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  367.14
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.95
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.01
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:03.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46000
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870000
  j =  1                              :        399908005
  j =  2                              :            45990
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908349
  j =  2                              :            45821
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.89e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.15
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17740.92
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.39
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.16
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.73
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.40
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.26
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  301.68
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.29
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.00
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.43
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.52
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999948245

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.63
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000061393

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:36.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52854812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.48
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:00:29.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.83
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.40
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45626
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869626
  j =  1                              :        399908752
  j =  2                              :            45618
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907607
  j =  2                              :            46186
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -7.33e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   13.30
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.90
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17373.13
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.52
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.85
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.31
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.56
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.42
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.16
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.57
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.54
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.34
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.02
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.99
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.61
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.31
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.54
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.28
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.88
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.43
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.25
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999961133

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.03
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000041947

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:58.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            0.9999 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53903388.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.98
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.64
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.36
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.76
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908569
  j =  2                              :            45711
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46067
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870067
  j =  1                              :        399907867
  j =  2                              :            46065
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.97e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17351.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.65
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.98
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.51
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.23
p-value of test                       :    0.9912


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.38
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.91
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.39
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.24
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.68e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3847.37
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.17
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000039208

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.31
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999993893

Normal statistic for number of bits   :  -0.048
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:13.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54886428.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:34.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:30.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.17
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:57.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908726
  j =  2                              :            45634
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908617
  j =  2                              :            45687
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.49e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.88e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17549.71
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   69.74
p-value of test                       :  4.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.29
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.42
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.09
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.72
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.72
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.61
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.39
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.68
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.27
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.06
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.67
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.35
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10272.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.11
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000060001

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.51
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999999095

Normal statistic for number of bits   : -7.15e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:32.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       4.3e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55902236.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:30.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.00
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.17
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45730
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869730
  j =  1                              :        399908543
  j =  2                              :            45724
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907604
  j =  2                              :            46192
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   36.07
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.94
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.033
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.15
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.63
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.20
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.84
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.81
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.91
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.58
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.73
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.47
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.17
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.84
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.84
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.36
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.78
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999935738

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.86
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999948275

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:12.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 59  WeightDistrib, r = 0            0.9993 
 74  RandomWalk1 J (L=50, r=0)       0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56885276.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5555
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.02
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.45
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:30.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.50
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908398
  j =  2                              :            45786
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.98
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.33
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.56
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.10
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.92
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.23
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  304.08
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.91
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.92
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:33.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5078.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.48
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.20
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999958841

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.60
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999992027

Normal statistic for number of bits   :  -0.063
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:28.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57966620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.08
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.86
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:30.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.51
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.81
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45511
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869511
  j =  1                              :        399908983
  j =  2                              :            45501
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908241
  j =  2                              :            45869
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:09.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.08
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17292.83
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.28
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.98
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.55
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.79
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.62
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.32
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.71
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.92
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.85
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.83
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.98
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 2.79e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9748.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:33.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.00
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4301.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.32
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.87
p-value of test                       :    0.9952


-----------------------------------------------
Total number of bits:  7999914117

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.46
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000022963

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:56.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58949660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:32.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9925

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9983

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.81
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.76
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908330
  j =  2                              :            45829
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908690
  j =  2                              :            45649
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:20.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:27.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.22
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.95
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.77
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.23
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.48
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.17
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.59
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.76
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.00
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.53
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5261.81
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.06
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.94
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.92
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.99
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -402.49
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.12
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 1.86e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11390.07
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.65
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999964391

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.44
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000111160

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:56.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59965468.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1219
p-value of test                       : 1 -  3.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334339
  j =  1                              :        599997562
  j =  2                              :             1219
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:32.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.15
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.49
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:28.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.23
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5165.19
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:56.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908340
  j =  2                              :            45824
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45532
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869532
  j =  1                              :        399908938
  j =  2                              :            45528
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.29e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.90
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.83
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.84
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.40
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.52
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.78
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.41
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.58
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.05
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.89
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.54
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.37
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.46
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.23
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.00
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.42
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.85
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.87
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999992369

Normal statistic for number of bits   :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.13
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000085186

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:45.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14          1 -  3.4e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60882972.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5309
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    3.89
p-value of test                       :  9.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:48.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.71
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.18
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.84
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908502
  j =  2                              :            45746
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907799
  j =  2                              :            46096
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.24e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:20.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.05
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.43
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:27.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.29
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:27.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.78
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.77
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.99
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.65
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.20
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.33
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.53
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.92
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.30
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.82
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.03

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.21
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.72
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.16
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12229.43
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.14
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999974357

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.28
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000007879

Normal statistic for number of bits   :   0.062
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:58.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61931548.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.61
p-value of test                       :  4.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    3.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.03
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:29.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:32.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.64
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5207.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908550
  j =  2                              :            45719
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908799
  j =  2                              :            45599
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.76e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:27.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17588.87
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.01
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.00
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.32
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.19
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.59
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.63
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.72
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.54
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.32
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.48
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.26
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.48
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.86
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.73
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.47
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.34
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999965390

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.16
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000139783

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    2.45
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.063
p-value of test                       :    0.53

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:37.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63012882.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    3.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.44
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:27.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.32
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908871
  j =  2                              :            45563
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908307
  j =  2                              :            45836
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.9e-3

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:28.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.33
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.93
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.53
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.21
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.38
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.44
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.70
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.53
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.14
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.07
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.03
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.68
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.02
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.67
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.14e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.07
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9705.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.42
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000196039

Normal statistic for number of bits   :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.52
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000001654

Normal statistic for number of bits   :   0.013
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:37.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43483165.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:19.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9956

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.07
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1335.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   90.16
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.80
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.10
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:50.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46259
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870259
  j =  1                              :        399907484
  j =  2                              :            46255
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908333
  j =  2                              :            45826
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:27.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.30
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  170.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17256.14
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.11
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.52
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.60
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.86
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.25
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.42
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.43
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.19
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.75
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.53
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.55
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.52
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.27
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.83e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.39
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.65
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000168928

Normal statistic for number of bits   :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.86
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000003496

Normal statistic for number of bits   :   0.028
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   0.084
p-value of test                       :    0.47

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:54.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44269574.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5550
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     262
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.07
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.46
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.79
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.16
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.71
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:19.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908181
  j =  2                              :            45905
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908189
  j =  2                              :            45904
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:28.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:27.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:33.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17625.38
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.89
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.97
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.11
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.35
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.43
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.17
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.59
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.71
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.39
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.76
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10252.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.54
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000002947

Normal statistic for number of bits   :   0.023
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.31
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999845231

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.19
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:43.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44990470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4526
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7092
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    3.45
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     254
p-value of test                       :    0.9964

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.96
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45617
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869617
  j =  1                              :        399908771
  j =  2                              :            45607
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908589
  j =  2                              :            45701
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:27.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:27.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17631.68
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.67
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.23
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.65
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.07
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5193.86
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.35
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.41
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.55
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.54
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.62
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.02
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9723.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11536.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.86
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999970040

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.99
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999971075

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.079
p-value of test                       :    0.47

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:24.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46530566.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5542
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:47.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.73
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:28.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.71
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.09
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908014
  j =  2                              :            45990
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908239
  j =  2                              :            45876
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.18e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.08
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.95
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   68.92
p-value of test                       :  5.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.60
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  417.12
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.99
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.73
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.67
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.75
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:32.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.20
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.48
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.02
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.26
p-value of test                       :    0.9961

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.19
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5109.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.11
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000122698

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.59
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000000283

Normal statistic for number of bits   : 2.24e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:03.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 M (L=50, r=0)       5.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47546374.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.99
p-value of test                       :  3.0e-3

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    5.50
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9970

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.86
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.69
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46238
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870238
  j =  1                              :        399907526
  j =  2                              :            46234
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908818
  j =  2                              :            45588
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   13.51
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17684.06
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.06
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.82
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.02
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.64
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.14
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.42
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.62
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.49
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:33.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.66
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.80
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.39
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000122248

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.26
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000188185

Normal statistic for number of bits   :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:47.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 43  Permutation, t = 10             0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48791558.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.77
p-value of test                       :  3.8e-3

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9928

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:28.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.64
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.49
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908053
  j =  2                              :            45966
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908661
  j =  2                              :            45659
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -6.83e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:26.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17465.52
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.96
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.12
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.10
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.66
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.58
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.71
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.32
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.32
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.96
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.73
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.47
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.25
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.24
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.01
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.91
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:01.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 3.61e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.15
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.53
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000170386

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.79
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999766733

Normal statistic for number of bits   :   -1.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.026
p-value of test                       :    0.49

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:17.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49840134.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9911


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7196.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:28.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.47
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.36
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908418
  j =  2                              :            45785
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908252
  j =  2                              :            45871
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    6.38
p-value of test                       :  6.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.9e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.10
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17596.20
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.06
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.56
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.87
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.70
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.35
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.63
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.33
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.57
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.60
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  474.26
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.84
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.27
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.65
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -403.00
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.96
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12071.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.80
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000140473

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.79
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000050356

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.19
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:26.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  2.9e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50855942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9940

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     663
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.42
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    5.99
p-value of test                       :  1.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  105.64
p-value of test                       :  2.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.83
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.35
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:59.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908185
  j =  2                              :            45900
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908071
  j =  2                              :            45963
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.81e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.39
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.12
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.91
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.35
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.60
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.92
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.26
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.55
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.84
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.55
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -402.46
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.84
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.48
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.63
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999928556

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.69
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999850895

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:53.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     2.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51871750.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:47.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    8.54
p-value of test                       :  7.1e-5    *****

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:17.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:47.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.98
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.86
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:47.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.62
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:28.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.72
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4854.69
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908430
  j =  2                              :            45782
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908025
  j =  2                              :            45986
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.89
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.94
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.62
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.54
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.80
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.86
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.19
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.45
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.80
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4853.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.09
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.06
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.79
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -402.35
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.39
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.81
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.53
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000078277

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.15
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999965459

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.06
p-value of test                       :    0.02

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:26.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           7.1e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52953094.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    3.01
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.53
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.10
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:47.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.00
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.27
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.98
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:45.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46541
p-value of test                       :  1.0e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870541
  j =  1                              :        399906922
  j =  2                              :            46533
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908118
  j =  2                              :            45935
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.99e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   16.69
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.50
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17176.93
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.06
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.20
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.89
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.65
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.99
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.06
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   35.07
p-value of test                       :  4.6e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  : -403.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.13
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.36
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.64
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.03
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.15
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.99
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000038029

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.05
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000060229

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.053
p-value of test                       :    0.48

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:24.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            5.0e-4
 80  LinearComp, r = 0              1 - eps1
 80  LinearComp, r = 0               4.6e-4
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53936134.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:50.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.04
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4862.46
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:02:47.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908286
  j =  2                              :            45848
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908791
  j =  2                              :            45594
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:12.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.04
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.26
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17314.64
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.74
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.17
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.95
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.97
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.64
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.75
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.21
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999823700

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.07
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999943802

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:46.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54951942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.99
p-value of test                       :  9.0e-3

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9957

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9944

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:49.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:20.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:29.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.75
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908174
  j =  2                              :            45910
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907879
  j =  2                              :            46056
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:12.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.10
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17612.85
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.95
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.36
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.96
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.06
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.19
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.89
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -403.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.83
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.02
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:34.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.02e-3
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4659.69
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.89
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999973100

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.59
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999902600

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:20.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55934982.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    3.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7238.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.30
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.39
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.72
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907964
  j =  2                              :            46003
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908491
  j =  2                              :            45750
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:10.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.03e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.68
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.87
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.96
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.99
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.03
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.21
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.01
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.30
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.81
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.64
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.87
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.27
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.53
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12023.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.83
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999917813

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.78
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999928472

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:26.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56918022.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    4.02
p-value of test                       :  8.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.51
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.23
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45524
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869524
  j =  1                              :        399908955
  j =  2                              :            45518
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908516
  j =  2                              :            45733
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -6.90e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17560.37
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.71
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.05
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.82
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.63
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.02
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.75
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.60
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.71
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.48
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.99
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.71
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.14
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.63
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.78
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.24
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.21
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000180547

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.73
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999986351

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:13.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57933830.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5598
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.47
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:46.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907700
  j =  2                              :            46147
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908369
  j =  2                              :            45811
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:20.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.60
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.86
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.87
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.58
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.71
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.46
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.47
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -403.33
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.45e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.54
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 1.87e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12110.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12172.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.48
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000087418

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.41
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000145753

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:32.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58916870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7055
p-value of test                       :    0.9990


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.95
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.01
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.97
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.49
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.36
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908506
  j =  2                              :            45744
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45477
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869477
  j =  1                              :        399909052
  j =  2                              :            45465
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:20.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.09e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.059
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17203.39
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.15
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.53
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.72
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.32
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.14
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.62
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.91
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.88
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.64
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.92
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.07
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.81
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.62
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:58.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4796.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.06
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000032218

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.54
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999962957

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.088
p-value of test                       :    0.54

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:31.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59768838.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:19.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    3.44
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.73
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7219.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.97
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.37
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.06
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:02:53.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908289
  j =  2                              :            45848
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907790
  j =  2                              :            46105
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    4.99
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:20.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.11e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17098.81
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.17
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.38
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.60
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.10
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.76
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.83
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.62
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.54
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.21
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -403.24
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.94e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.97
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.66
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3891.96
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.15
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.77
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999983255

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.57
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999935819

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:35.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60850182.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.50
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     347
p-value of test                       :  4.3e-3

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6863.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.38
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908445
  j =  2                              :            45776
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908215
  j =  2                              :            45885
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:20.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:21.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:13.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.09
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.37
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.33
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.82
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.39
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.21
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.57
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.06
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.50
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.90
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.21
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.14
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.61
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.75
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.77
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.35
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.99
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11990.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12233.01
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.62
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999788315

Normal statistic for number of bits   :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.81
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000003163

Normal statistic for number of bits   :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:05.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61865990.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:18.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:23.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.16
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     545
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.44
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:30.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.92
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.11
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:46.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908531
  j =  2                              :            45730
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45074
p-value of test                       : 1 -  8.2e-5    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869074
  j =  1                              :        399909855
  j =  2                              :            45068
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:20.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17084.10
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.99
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.35
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.89
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.48
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.56
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.79
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.58
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.00
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.01
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.28
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.16e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.29
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.81
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12129.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.11
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999973583

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.95
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000010993

Normal statistic for number of bits   :   0.087
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:59.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 45  CollisionPermut, r = 10        1 -  8.2e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62881798.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.71
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:39.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.51
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1329.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.09
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5214.02
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908184
  j =  2                              :            45902
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907892
  j =  2                              :            46048
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9951


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9940


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.020
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:28.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.70
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.44
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.85
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.47
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.69
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.99
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.03
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:32.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.12
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.12e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.42
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.94
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.73
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.86
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.31
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999871505

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.32
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000023950

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.096
p-value of test                       :    0.54

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:26.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43515934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:30.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.15
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908399
  j =  2                              :            45790
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908824
  j =  2                              :            45582
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:20.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:21.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:33.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.74
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.69
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.62
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.26
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.10
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.87
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.59
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.00
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.87
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.33
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.40
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999972122

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.82
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999985703

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:18.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44531742.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.86
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    3.63
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:38.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6878.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.47
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.62
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:30.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.58
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45472
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869472
  j =  1                              :        399909059
  j =  2                              :            45466
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908468
  j =  2                              :            45763
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    5.55
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.81e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:20.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:27.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17805.58
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.22
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.19
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.38
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.71
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.27
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.21
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.64
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.12
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  481.13
p-value of test                       :  5.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.15
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.99
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.50
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.21
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  : -401.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.05e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.19
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9815.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:39.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.57
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999891944

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.07
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999935216

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:41.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 H (L=10000, r=0)    5.4e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45514782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:17.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.19
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     674
p-value of test                       :  1.6e-3

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:10.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7355.89
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:30.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:59.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908422
  j =  2                              :            45780
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46025
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870025
  j =  1                              :        399907951
  j =  2                              :            46023
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.66e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:28.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:34.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.82
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.05
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.25
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   38.82
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.72
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.83
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.11
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.25
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.86e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.04
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9819.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11571.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999846695

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.99
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000085864

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:06.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46563358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5311
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:11.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.21
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:46.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   17.37
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:00:29.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:49.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908436
  j =  2                              :            45779
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907771
  j =  2                              :            46110
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:32.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.26
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.24
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.57
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.33
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.58
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:32.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.81
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.03
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -402.34
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.87
p-value of test                       :  2.0e-3

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.29
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.06
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.30
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.69
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999980816

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.32
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000000931

Normal statistic for number of bits   : 7.36e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:47.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47611934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6775.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.44
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.37
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.11
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.05
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:53.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908264
  j =  2                              :            45865
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908205
  j =  2                              :            45893
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:26.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.61
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.53
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.14
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.32
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.51
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.32
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.79
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.41
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.85
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.96
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.25
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.15
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.68
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.43
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.29
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.32
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999919544

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.84
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999984464

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:08.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48660510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.88
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.87
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:20.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:29.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.09
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.65
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:55.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908506
  j =  2                              :            45744
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908535
  j =  2                              :            45725
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.73
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.18
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  204.84
p-value of test                       :  9.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.83
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.96
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.44
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.29
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.00
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.81
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -403.05
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.26
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -403.22
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.06
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.13
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.49
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.69
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4296.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12260.23
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.50
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000083305

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.58
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000041482

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.64
p-value of test                       :  4.1e-3

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:38.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     9.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49709086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:13.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.59
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:29.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.57
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.78
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:55.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908116
  j =  2                              :            45936
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907821
  j =  2                              :            46085
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:14.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.39
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.50
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.78
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.56
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.33
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.97
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.54
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.35
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.26
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.35
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.99
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.02
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.63
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.61
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.28
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4659.72
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.13
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.78
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999915707

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.57
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000115834

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.15

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.015
p-value of test                       :    0.51

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:28.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50757662.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5559
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     653
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:48.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.31
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:29.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.55
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.28
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:52.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908114
  j =  2                              :            45940
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908336
  j =  2                              :            45829
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.15e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17061.72
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.12
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.94
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.14
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.36
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.70
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.40
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.05
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.11
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.17e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.04
p-value of test                       :    0.9980

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.06
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5087.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.02
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999882911

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.49
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000047272

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:00.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51806238.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:21.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:27.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.90
p-value of test                       :  9.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6896.22
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:28.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.22
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.09
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908454
  j =  2                              :            45767
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908453
  j =  2                              :            45769
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9999    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:21.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:14.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:31.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:31.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17108.20
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.94
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.07
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.49
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.40
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.95
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.29
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.62
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.57
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.09
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  : -402.70
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.01
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.29
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.52
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000064807

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.46
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000011062

Normal statistic for number of bits   :   0.087
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:37.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52887582.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6850.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.68
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908081
  j =  2                              :            45955
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46138
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870138
  j =  1                              :        399907730
  j =  2                              :            46126
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.44
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:00:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.17
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.81
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.99
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.29
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.74
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.01
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.33
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.31
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.96
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.01
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.63
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.84
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.63
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.76
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999948719

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.61
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999947588

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:04.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54067230.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.24
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:47.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.12
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:28.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.58
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908498
  j =  2                              :            45748
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908107
  j =  2                              :            45939
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:14.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.23
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.07
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.11
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.45
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5281.94
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.42
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.34
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.24
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.02
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.07
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.15
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:34.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.11
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999908306

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.38
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000076813

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:03.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55083038.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:27.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7129
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:16.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.83
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9911

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.99
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:28.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.91
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45452
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869452
  j =  1                              :        399909097
  j =  2                              :            45450
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908603
  j =  2                              :            45697
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.12e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:31.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:30.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17179.87
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.49
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.58
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.58
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.83
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  179.70
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.79
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.61
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.95
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.23
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.54
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.05
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.91
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.56
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.13
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10255.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3932.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.41
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999960386

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.14
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999931415

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:38.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56164382.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    3.27
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     112
p-value of test                       :    0.9993    *****

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:50.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6821.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.10
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.30
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908626
  j =  2                              :            45684
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45595
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869595
  j =  1                              :        399908813
  j =  2                              :            45589
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.42e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:31.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.50
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.64
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.83
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.39
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4804.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.85
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.75
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.26
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  457.07
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.89
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -403.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.54
p-value of test                       :    0.9903


-----------------------------------------------
Normal statistic for number of jumps  : -402.69
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.78
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.28
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.91
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000085012

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.14
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999968465

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.024
p-value of test                       :    0.49

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:26.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16       0.9993 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57180190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7538
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9963


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:46.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   38.62
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.69
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.56
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4809.38
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45505
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869505
  j =  1                              :        399908994
  j =  2                              :            45497
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907799
  j =  2                              :            46093
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:21.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:31.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.03e-3
p-value of test                       :    0.9990

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.35
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17507.99
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.16
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.31
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.98
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.60
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.34
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.73
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.35
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.06
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.27e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.86
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.45
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999929981

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999867908

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:01.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58228766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:36.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:19.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9940

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.57
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.88
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.63
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:29.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.61
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.84
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908396
  j =  2                              :            45796
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908713
  j =  2                              :            45636
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:13.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.76
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17629.75
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.55
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   94.93
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   44.21
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.29
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.91
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.02
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.00
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.54
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5282.80
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.73
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:32.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4742.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.67
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3918.99
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.16
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000100399

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.22
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000023140

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:16.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 27  SimpPoker, r = 27               0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59277342.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4512
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    5.43
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.79
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.89
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908839
  j =  2                              :            45576
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45569
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869569
  j =  1                              :        399908864
  j =  2                              :            45565
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17135.09
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.29
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.37
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.46
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  434.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.45
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.93
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.19
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:33.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.74
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.32
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.41
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.42
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.29
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000013246

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.51
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999951563

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.13
p-value of test                       :    0.98

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:11.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60293150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:28.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     964
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    3.95
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:02:48.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1311.60
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.41
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:19.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:29.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.43
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.46
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908820
  j =  2                              :            45587
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907679
  j =  2                              :            46153
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-5
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    : 3.72e-4
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    4.93
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:32.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.33
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.88
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.89
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.16
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.35
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.59
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.00
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.05
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4810.49
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.81
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:32.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.29
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.45
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.78
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:42.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10139.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.40
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.092
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5090.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3993.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11511.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.81
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000100039

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.80
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000032260

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:18.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61308958.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5551
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:33.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.81
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:28.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.40
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907775
  j =  2                              :            46099
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908190
  j =  2                              :            45899
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.87e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:26.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.21
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.83
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.83
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.22
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.97
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.95
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.56
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.24
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.87
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.55
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.37
p-value of test                       :    0.9986


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.95
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.18e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.15
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:02.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.76
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.26
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999914459

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.87
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000112114

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.045
p-value of test                       :    0.52

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:10.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62423070.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:47.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1223
p-value of test                       : 1 -  5.3e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334343
  j =  1                              :        599997554
  j =  2                              :             1223
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.90
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6916.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.71
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.03
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908427
  j =  2                              :            45779
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45521
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869521
  j =  1                              :        399908963
  j =  2                              :            45511
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:30.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:30.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.16
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.85
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.44
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.88
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.55
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.64
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.31
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.46
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -402.83
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.61e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   28.56
p-value of test                       :  3.8e-4    *****

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.13
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11528.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.76
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999993158

Normal statistic for number of bits   :  -0.054
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.69
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999936896

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.18
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:41:44.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14          1 -  5.3e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 86  LongestHeadRun, r = 0           3.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63438878.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1213
p-value of test                       : 1 -  1.6e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334333
  j =  1                              :        599997574
  j =  2                              :             1213
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:33.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4509
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:18.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.66
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   50.55
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.01
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.26
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.00
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908071
  j =  2                              :            45957
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907704
  j =  2                              :            46142
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:13.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:28.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.88
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.89
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.90
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4775.08
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.39
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.55
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.12
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.15
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  : -402.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.57
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.84
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.17
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.92
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999960023

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.33
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999976889

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:51:41.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14          1 -  1.6e-5
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43548703.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:39.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   21.17
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.10
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908651
  j =  2                              :            45670
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908132
  j =  2                              :            45931
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.35e-6
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.49
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:13.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:28.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.89
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   39.14
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.48
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.96
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.34
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.31
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.00
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.78
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.67
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:33.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.78
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.00e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.36
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  253.26
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9760.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:42.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10216.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4723.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4266.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.86
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000043960

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.37
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999752276

Normal statistic for number of bits   :   -1.96
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    3.01
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:14.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44400671.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:40.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.16
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     966
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.35
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.31
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.37
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:54.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908634
  j =  2                              :            45683
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46177
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870177
  j =  1                              :        399907647
  j =  2                              :            46175
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.10e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:27.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.97
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   62.98
p-value of test                       :  3.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.16
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.28
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.12
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.93
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.50
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.31
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.92
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.14
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.65
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:32.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.77
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.23
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -402.91
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.91
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10361.44
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.15
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.48
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000127168

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.81
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999920378

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:59.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            0.9992 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45350943.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7079
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:18.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:36.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6941.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.80
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.06
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908428
  j =  2                              :            45780
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908455
  j =  2                              :            45768
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-5
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:20.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:27.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:27.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17527.92
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.72
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.06
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.77
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.58
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.02
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.23
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.22
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.23
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.60
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.91
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  : -402.85
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.60
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5096.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.30
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000022843

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.42
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999965555

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:03.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46235679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:32.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    2.84
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     834
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.12
p-value of test                       :    0.9998    *****

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7271.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.38
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:31.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.94
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.06
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:48.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908460
  j =  2                              :            45767
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908790
  j =  2                              :            45596
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:20.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:33.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:27.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.048
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.81
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.79
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.83
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.87
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.68
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.42
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.50
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  : -403.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3881.56
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000086728

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.96
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000191650

Normal statistic for number of bits   :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:42.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP, t = 5           0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47120415.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997305
  j =  2                              :             1346
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:33.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4497
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.93
p-value of test                       :  9.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.34
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     971
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:39.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:31.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.69
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.11
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908167
  j =  2                              :            45909
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46214
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870214
  j =  1                              :        399907579
  j =  2                              :            46200
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.21e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.22
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:26.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:27.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.44
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17655.38
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.62
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.24
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.41
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.84
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.17
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  471.53
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.77
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.42
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.85
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.55
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.49
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.35
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  : -402.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.93
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  : -402.76
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.33
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.9927

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.75
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000054523

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.91
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000000187

Normal statistic for number of bits   : 1.48e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:09.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               0.9994 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48168991.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5583
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:32.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4497
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    4.04
p-value of test                       :  8.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    3.88
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:38.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6884.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.29
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   79.16
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4748.30
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45631
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869631
  j =  1                              :        399908740
  j =  2                              :            45627
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:33.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.47
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.04
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.58
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.89
p-value of test                       :    0.9967


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.45
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.66
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.11
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -403.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.94
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  2.9e-4    *****

Anderson-Darling statistic = A2       :    5.38
p-value of test                       :  2.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  262.70
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.31e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  150.58
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.88
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.36
p-value of test                       :  6.3e-3


-----------------------------------------------
Total number of bits:  8000133804

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.79
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999988949

Normal statistic for number of bits   :  -0.087
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.090
p-value of test                       :    0.54

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:38.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49250335.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.21
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.67
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.28
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:32.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.97
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908253
  j =  2                              :            45869
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908109
  j =  2                              :            45941
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:20.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:13.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:13.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:27.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:28.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.87
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.02
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.99
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.71
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.30
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.02
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.85
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.44
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.79
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.82
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.28
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.28
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  : -402.93
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  : -402.54
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.27e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   25.86
p-value of test                       :  1.1e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:33.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.37
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000040756

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.65
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999943433

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:15.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50135071.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7090
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:45.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.69
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.92
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.68
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.71
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908822
  j =  2                              :            45580
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907690
  j =  2                              :            46149
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:20.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:26.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:32.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:33.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:33.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:33.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.38
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.30
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.37
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.23
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.65
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.16
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.94
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.34
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.33
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.25
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.02
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.12
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.16
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.91
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.27
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.98
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.13
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    4.85
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.28
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000003721

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.80
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000039880

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.9950

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.8e-3

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:44.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51183647.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:32.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7108
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9933

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:15.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7159.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.84
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.01
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.54
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:47.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908351
  j =  2                              :            45817
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45500
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869500
  j =  1                              :        399909003
  j =  2                              :            45494
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:14.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:33.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:33.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:33.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17631.99
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.80
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.09
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.36
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.19
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.14
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  148.06
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.80
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.40
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.56
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999884528

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.31
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999959063

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.02e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:43.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52559903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1503
p-value of test                       :  1.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334623
  j =  1                              :        599996994
  j =  2                              :             1503
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:32.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7508
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.93
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:31.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5253.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908842
  j =  2                              :            45570
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907541
  j =  2                              :            46225
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:20.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:13.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:32.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:26.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17225.28
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.09
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.84
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.60
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.52
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.25
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:34.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.02
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.12
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.45
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.37
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.70
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -401.81
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.21
p-value of test                       :  4.5e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9662.10
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4679.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.36
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000039430

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.05
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999927989

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:42.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           1.1e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53510175.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908329
  j =  2                              :            45831
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908615
  j =  2                              :            45685
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:33.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.10
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.10
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.02
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.64
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  458.47
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.04
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  : -402.38
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.99
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.34
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999939755

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.40
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999925187

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:45:54.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54591519.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:20.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7586
p-value of test                       :  9.5e-4    *****


-----------------------------------------------
CPU time used                    :  00:04:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9912


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:50.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:29.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.52
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.50
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908082
  j =  2                              :            45956
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46187
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870187
  j =  1                              :        399907628
  j =  2                              :            46183
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.55e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.75e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17156.77
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.39
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.43
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.85
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.73
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.39
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.58
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.30
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.09
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.40
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.43
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4312.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.71
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.98
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000079747

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.63
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000051739

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Tests on the sum of all N observations
Standardized normal statistic         :   0.031
p-value of test                       :    0.49

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:50:57.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        9.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55607327.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5530
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.40
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:47.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  491.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.12
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4912.29
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908090
  j =  2                              :            45946
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46311
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870311
  j =  1                              :        399907378
  j =  2                              :            46311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:35.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:21.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:31.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:31.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.60
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.61
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.26
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.18
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.28
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.73
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.11
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.43
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.36
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.96
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:33.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.52
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.38
p-value of test                       :  3.5e-3


-----------------------------------------------
Normal statistic for number of jumps  : -403.29
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.56
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000091099

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.58
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999872666

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:39.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57147423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9978


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:48.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:29.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.35
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.29
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908090
  j =  2                              :            45952
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908670
  j =  2                              :            45659
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-5
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    : 4.68e-4
p-value of test                       :  1.6e-4    *****

Anderson-Darling statistic = A2       :    7.12
p-value of test                       :  3.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:21.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:31.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:31.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.73
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   99.90
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17499.14
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.66
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.02
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.33
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.66
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.00
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.32
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.59
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.71
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5262.71
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.99
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:32.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.82
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  : -402.96
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.69
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.84
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4221.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11596.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.58
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999955814

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.37
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999975746

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.19
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:59.44
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               3.0e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58163231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:47.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:45.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    3.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     668
p-value of test                       :  3.3e-3

Stat. AD (mNP2)                       :    3.14
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.08
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  373.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:16.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.58
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:29.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.38
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.99
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908284
  j =  2                              :            45855
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908048
  j =  2                              :            45970
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:21.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:21.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.60
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.05
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.92
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.47
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.66
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:33.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4785.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.30
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.96
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.52
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.28
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  : -402.59
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.99

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.53
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:01.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.23
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12074.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.71
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000009661

Normal statistic for number of bits   :   0.076
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.85
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999963923

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:45.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59211807.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9920

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.60
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.12
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:29.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.57
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.27
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46213
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870213
  j =  1                              :        399907576
  j =  2                              :            46209
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908368
  j =  2                              :            45810
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:12.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:21.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:14.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:27.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:32.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:27.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.66
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.07
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.13
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.14
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.33
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.65
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.47
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.42
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.69
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  : -401.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.01
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  : -402.63
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.92e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.35
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.99
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.31
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.07
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999869594

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.26
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000081625

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:33.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60194847.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:29.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908212
  j =  2                              :            45885
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908615
  j =  2                              :            45685
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:21.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.00
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17194.50
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.11
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.02
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.78
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.42
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.45
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.15
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.32
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.96
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.06
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.27
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.92
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.58
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.74
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -401.72
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.71
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.36
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11710.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.13
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999957674

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.99
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000123880

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:06.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61341727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:33.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:47.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.44
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:30.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.92
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.55
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:59.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45647
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869647
  j =  1                              :        399908711
  j =  2                              :            45637
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907718
  j =  2                              :            46138
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:11.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:21.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.03
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:25.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17158.61
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:48.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.45
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.38
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.76
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.31
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.77
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.99
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.98
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.37
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  : -402.42
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10147.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:32.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.10
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000105802

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.87
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000095554

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:16.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62390303.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.14
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:45.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.46
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.99
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:30.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.23
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46174
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870174
  j =  1                              :        399907658
  j =  2                              :            46162
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908375
  j =  2                              :            45805
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 5.78e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.23e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:13.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:13.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:31.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:31.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.24
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.82
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.74
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.20
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.33
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.82
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.10
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.54
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  : -402.75
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.38
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -402.56
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.83e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.24
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:22.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.49
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000037006

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.38
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000060460

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:28.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2S, t = 5         0.9991 
 75  RandomWalk1 H (L=50, r=25)      0.9991 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 63373343.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5602
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:03:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:24.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    3.26
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     257
p-value of test                       :    0.9939

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:36.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1562.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.63
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:31.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.20
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.78
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907789
  j =  2                              :            46101
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908141
  j =  2                              :            45925
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-5
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:14.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:28.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:28.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.30
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17361.69
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.93
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.44
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.54
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.23
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.52
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.11
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.82
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.57
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.07
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.72
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.77
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:32.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.85
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  : -402.47
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  : -403.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.20
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.34
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.049
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4289.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.93
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999958295

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.19
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000048349

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:52:10.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43581472.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1500
p-value of test                       :  1.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334620
  j =  1                              :        599997000
  j =  2                              :             1500
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:39.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:30.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.61
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.06
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908141
  j =  2                              :            45922
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908389
  j =  2                              :            45795
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:33.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17088.38
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:51.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.19
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.08
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.00
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.00
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.87
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.95
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.45
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.33
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.06
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:32.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : -402.18
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  : -402.84
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.90
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:02.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:34.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.31
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000051547

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.62
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999986798

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.061
p-value of test                       :    0.52

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:45.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           1.5e-4
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44466208.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:02:39.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.00
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  171.09
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6922.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:30.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.22
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.43
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:00.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45437
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869437
  j =  1                              :        399909131
  j =  2                              :            45427
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908558
  j =  2                              :            45715
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:09.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:14.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:28.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:27.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.38
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17329.44
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.57
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.19
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.36
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.23
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.17
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.00
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.85
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.67
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:31.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.48
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  : -403.02
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:33.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.45
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000062494

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.43
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000173194

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:10.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45580320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:28.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:45.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:47.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:19.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    4.28
p-value of test                       :  6.4e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1342.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:29.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5127.25
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907843
  j =  2                              :            46071
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908012
  j =  2                              :            45991
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:10.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:14.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:14.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:27.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:33.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:33.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:31.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17695.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.77
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.35
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.33
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.57
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.52
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.33
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:32.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:32.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.49
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : -402.17
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.44
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.65e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:03.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9636.02
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.91
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.83
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4633.98
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.48
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000054796

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.15
p-value of test                       :    0.9921


-----------------------------------------------
Total number of bits:  8000130342

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:49:30.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46497824.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.85
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907910
  j =  2                              :            46042
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908051
  j =  2                              :            45970
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.13e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:27.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:33.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:32.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:32.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.32
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.72
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.29
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.41
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.06
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.16
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:32.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.83
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.67
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.45
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  : -402.82
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.01
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.96
p-value of test                       :  3.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.89
p-value of test                       :    0.9981

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.41e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:39.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.80
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.35
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999928199

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.85
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999921098

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:02.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47644704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5568
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.22
p-value of test                       :  6.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    4.05
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.81
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:29.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.34
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.08
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45348
p-value of test                       :    0.9935


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869348
  j =  1                              :        399909306
  j =  2                              :            45344
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908818
  j =  2                              :            45585
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:21.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -5.96e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:14.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:32.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  172.70
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17631.30
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.89
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.57
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.21
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.67
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.25
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.45
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.22
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.16
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.13
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.93
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  : -403.23
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  : -403.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.74
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9715.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.85
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.12
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000147970

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.33
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000127315

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:47:55.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48594976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9927

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.81
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.29
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6817.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:29.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.28
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.95
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908526
  j =  2                              :            45731
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46139
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870139
  j =  1                              :        399907724
  j =  2                              :            46135
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:33.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:21.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:14.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:14.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.49
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:33.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.83e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17118.18
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.83
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.69
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.63
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.05
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.83
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.33
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.93
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:32.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.54
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:32.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.28
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  : -402.26
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.24
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  : -402.77
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.21
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:36.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.57
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999988010

Normal statistic for number of bits   :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.64
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999944330

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.31
p-value of test                       :    0.99

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:17.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49676320.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4513
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:09.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:29.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.53
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.66
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908584
  j =  2                              :            45705
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908455
  j =  2                              :            45768
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:11.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.23e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.70e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:14.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.50e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:28.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:27.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.53
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.42
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.13
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.61
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.00
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.06
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.21
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.73
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.28
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:32.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -402.79
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.56
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.68
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.68
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4320.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.35
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000096796

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.51
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000122941

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  3.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.11
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:48:38.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50724896.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:48.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     651
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:47.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7311.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.51
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.71
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908457
  j =  2                              :            45764
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908079
  j =  2                              :            45953
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:14.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:26.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:32.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:31.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.28
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.14
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.75
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.48
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.81
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.17
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  419.73
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.00
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.61
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.45
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.27
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.10
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:33.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.06
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.80
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.36
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  : -403.16
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  : -402.89
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.41
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.28
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999948488

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.90
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999984554

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:34.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51904544.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:47.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:47.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:28.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.65
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907810
  j =  2                              :            46089
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908637
  j =  2                              :            45680
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.70e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:21.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:14.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:14.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.05
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:00:26.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.21
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:31.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.88
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17532.61
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.91
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.55
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.09
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.91
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.80
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.61
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.86
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.64
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.70
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.89
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.05
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:32.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.28
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.22
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.97
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.55
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.08
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  : -402.67
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.49
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  : -401.86
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.19
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.35
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000152674

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.13
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000063544

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:52.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52920352.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:48.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:25.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:26.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9913

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:02:13.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.52
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7233.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.39
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4848.41
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46241
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870241
  j =  1                              :        399907522
  j =  2                              :            46233
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908089
  j =  2                              :            45951
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:12.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.55e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:14.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:32.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:31.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:25.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:31.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.76
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.41
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.38
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.49
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.08
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:33.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.59
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.06
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.03
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  : -402.50
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  : -402.31
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.37e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.80
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.90
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000179824

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.38
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000115138

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    2.41
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:15.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53968928.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.6e-3


-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.16
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:48.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.56
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:29.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908692
  j =  2                              :            45648
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908116
  j =  2                              :            45942
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:12.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:21.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:15.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:15.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.64
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:31.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17208.24
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.14
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.89
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.10
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.86
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.11
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.96
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.76
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.32
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.44
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -403.03
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.70
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  : -402.51
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:02.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12035.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.49
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999981827

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.89
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000127840

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:46:03.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54984736.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:44.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.13
p-value of test                       :    0.9996    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:47.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.35
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.91
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:19.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:29.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.66
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.07
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907948
  j =  2                              :            46020
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908220
  j =  2                              :            45884
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:21.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.91e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:14.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.79
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:31.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.09
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.95
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.21
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.80
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.48
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.74
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  : -402.44
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  : -402.74
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.13e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.61e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.34
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.40
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.13
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 5.02e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5194.90
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.60
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999928568

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.86
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000001399

Normal statistic for number of bits   :   0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:36.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            0.9996 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56000544.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:33.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:17.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:46.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.96
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:29.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.47
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.16
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908453
  j =  2                              :            45766
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908140
  j =  2                              :            45927
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:21.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 3.30e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:21.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:14.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:31.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17142.21
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.21
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.00
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.98
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.99
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.65
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.83
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.53
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.11
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:33.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.24
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5037.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.86
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.40
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  : -402.48
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  : -402.55
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.37
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10235.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:38.87

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.51
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999989381

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.10
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000125671

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:43.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56983584.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    3.61
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     347
p-value of test                       :  4.3e-3

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9937

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:48.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.10
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.47
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6922.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.77
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:29.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.30
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.39
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908128
  j =  2                              :            45930
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908813
  j =  2                              :            45586
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.41e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:21.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:14.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:25.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:31.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.80
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   56.22
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.36
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.96
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.79
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.87
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.78
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.82
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  573.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.22
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.27
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.99
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:33.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.67
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.06
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.06
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -403.04
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.56
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  : -402.64
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:42.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.72
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5004.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.46
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.91
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999836165

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.58
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999854423

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:15.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58064928.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.33
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:45.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6852.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.53
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:29.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.39
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46208
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870208
  j =  1                              :        399907587
  j =  2                              :            46202
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907999
  j =  2                              :            45987
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.32e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:21.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:13.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.15
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:32.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.40
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17383.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.29
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.29
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  200.93
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.47
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.57
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.98
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.52
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.66
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.23
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.13
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.14
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.48
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.79
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:33.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : -402.90
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  : -402.52
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:42.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.06
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.20
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11544.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.95
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999991397

Normal statistic for number of bits   :  -0.068
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.93
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999954137

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:44:17.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59146272.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997299
  j =  2                              :             1349
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:15.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     119
p-value of test                       :    0.9949

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.01
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.51
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.75
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907898
  j =  2                              :            46045
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907835
  j =  2                              :            46078
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    : 3.49e-4
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:14.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:29.30

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:31.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:31.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:25.90

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:32.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:32.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17759.14
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.83
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.15
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:42.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.48
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.21
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.96
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.67
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.25
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  : -402.14
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.81
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  : -402.20
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:42.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.44
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.96
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11598.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.96
p-value of test                       :  1.9e-3


-----------------------------------------------
Total number of bits:  8000113293

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000050005

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         : -1.96e-3
p-value of test                       :    0.50

Sample variance                       :    0.21
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:43:41.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60162080.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:33.61

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:28.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:46.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:29.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.33
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.72
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:00.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908538
  j =  2                              :            45722
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908351
  j =  2                              :            45817
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:21.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:14.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:14.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.39
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:32.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:26.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:32.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17136.47
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.30
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.71
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.83
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:33.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.74
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:33.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.10
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  : -402.97
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.75
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  : -402.21
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.63e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.28
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.13
p-value of test                       :  2.3e-3


-----------------------------------------------
Total number of bits:  7999962981

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.84
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000032287

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.56
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:52.65
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61276192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997187
  j =  2                              :             1405
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.83
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:30.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.08
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.16
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907992
  j =  2                              :            45998
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908501
  j =  2                              :            45745
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:21.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.09e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:21.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:13.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:32.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:32.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:26.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:31.92

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:31.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.90
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.22
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.48
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.11
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.56
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.81
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.36
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4764.53
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  458.43
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.63
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:32.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.64
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -402.94
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -402.10
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.31

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:42.51

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.66e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.31
p-value of test                       :  9.2e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:32.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.23
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11800.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.57
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999951773

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.26
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000034867

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:42:26.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               0.9998 
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62357536.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n96, Linux

MT19937


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4201
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1570.45
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:52.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.95
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908351
  j =  2                              :            45817
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n96, Linux

MT19937


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45494
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869494
  j =  1                              :        399909015
  j =  2                              :            45488
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.73

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:11.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:20.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:21.34

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:13.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:13.88

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:25.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:31.96

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:31.60

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:31.69

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.96
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.12
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.41
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.95
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.04
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.61
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.94
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.36
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:32.84

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:32.59

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.40
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  : -402.68
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.21

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.03
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  : -402.57
p-value of test                       : 1 - eps1    *****



-----------------------------------------------
CPU time used                    :  00:00:06.19

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.24
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.19
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:23.50

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.06
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.76
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999907106

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.49
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000059380

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.01

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n96, Linux

MT19937


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        MT19937
 Number of statistics:  160
 Total CPU time:   02:40:37.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0              1 - eps1
 81  LinearComp, r = 29             1 - eps1
 ----------------------------------------------
 All other tests were passed




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